53 results on '"Samson L. Shatashvili"'
Search Results
2. Characters, coadjoint orbits and Duistermaat-Heckman integrals
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Samson L. Shatashvili and Anton Alekseev
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High Energy Physics - Theory ,Pure mathematics ,FOS: Physical sciences ,General Physics and Astronomy ,Lie group ,Minimal models ,Loop (topology) ,High Energy Physics::Theory ,High Energy Physics - Theory (hep-th) ,Factorization ,Mathematics - Symplectic Geometry ,Mathematics::Quantum Algebra ,Irreducible representation ,Mathematics - Quantum Algebra ,FOS: Mathematics ,Quantum Algebra (math.QA) ,Symplectic Geometry (math.SG) ,Virasoro algebra ,Geometry and Topology ,Invariant (mathematics) ,Mathematics::Representation Theory ,Mathematics::Symplectic Geometry ,Mathematical Physics ,Symplectic geometry ,Mathematics - Abstract
The asymptotics of characters $\chi_{k\lambda}(\exp(h/k))$ of irreducible representations of a compact Lie group $G$ for large values of the scaling factor $k$ are given by Duistermaat-Heckman (DH) integrals over coadjoint orbits of $G$. This phenomenon generalises to coadjoint orbits of central extensions of loop groups $\widehat{LG}$ and of diffeomorphisms of the circle $\widehat{\rm Diff}(S^1)$. We show that the asymptotics of characters of integrable modules of affine Kac-Moody algebras and of the Virasoro algebra factorize into a divergent contribution of the standard form and a convergent contribution which can be interpreted as a formal DH orbital integral. For some Virasoro modules, our results match the formal DH integrals recently computed by Stanford and Witten. In this case, the $k$-scaling has the same origin as the one which gives rise to classical conformal blocks. Furthermore, we consider reduced spaces of Virasoro coadjoint orbits and we suggest a new invariant which replaces symplectic volume in the infinite dimensional situation. We also consider other modules of the Virasoro algebra (in particular, the modules corresponding to minimal models) and we obtain DH-type expressions which do not correspond to any Virasoro coadjoint orbits. We study volume functions $V(x)$ corresponding to formal DH integrals over coadjoint orbits of the Virasoro algebra. We show that they are related by the Hankel transform to spectral densities $\rho(E)$ recently studied by Saad, Shenker and Stanford., Comment: 27 pages, new material is added, references added
- Published
- 2021
3. Ludwig Dmitrievich Faddeev (obituary)
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Valerii Vasil'evich Kozlov, I. Ya. Aref'eva, N. Yu. Reshetikhin, Igor Krichever, L. A. Takhtajan, F. A. Smirnov, Sergey Novikov, Evgeny Sklyanin, Vladimir E. Zakharov, Michael Semenov-Tian-Shansky, Alexander M. Polyakov, Samson L. Shatashvili, and V. P. Maslov
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General Mathematics ,Theology ,Obituary ,Mathematics - Published
- 2017
4. Scientific heritage of L.D. Faddeev. Survey of papers
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M. A. Semenov-Tian-Shansky, I. Ya. Aref'eva, Evgeny Sklyanin, A. Yu. Alekseev, Samson L. Shatashvili, F. A. Smirnov, Leon A. Takhtajan, Euler International Mathematical Institute [St. Petersburg], Stony Brook University [SUNY] (SBU), State University of New York (SUNY), University of Geneva [Switzerland], Steklov Mathematical Institute [Moscow] (SMI), Russian Academy of Sciences [Moscow] (RAS), Institut de Mathématiques de Bourgogne [Dijon] (IMB), Centre National de la Recherche Scientifique (CNRS)-Université de Franche-Comté (UFC), Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université de Bourgogne (UB), University of York [York, UK], Université Pierre et Marie Curie - Paris 6 (UPMC), Institut des Hautes Etudes Scientifiques (IHES), IHES, Trinity College Dublin, Institute for Information Transmission Problems, The work of Semenov-Tian-Shansky was supported by the Presidium of the Russian Academy of Sciences programme no. 02 'Non-linear dynamics: fundamental problems and applications' (grant no. PRAS-18-02). Sklyanin worked as a Royal Society Leverhulme Trust Senior Research Fellow. The work of Shatashvili was supported by the Simons Foundation under the programme 'Targeted Grants to Institutes' (The Hamilton Mathematics Institute)., Université de Genève = University of Geneva (UNIGE), Université de Bourgogne (UB)-Université Bourgogne Franche-Comté [COMUE] (UBFC)-Centre National de la Recherche Scientifique (CNRS), and Institut des Hautes Études Scientifiques (IHES)
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Inverse scattering problem ,Scattering theory ,General Mathematics ,Yang-Baxter equation ,Inverse scattering method ,Quantum groups ,01 natural sciences ,AMS 2010 Mathematics Subject Classification. Primary 01A70, 16T25, 17B37, 35J10, 35P25,35Q53, 35Q55, 37K15, 58B32, 58J52, 70S15, 81-03, 81R50, 81S40, 81T10, 81T13, 81T50, 81T70,81U40, 82B23, 82C23 ,Eigenfunction expansion ,[MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph] ,Quantization of gauge fields ,Korteweg-de Vries equation ,0103 physical sciences ,Schrodinger operator ,0101 mathematics ,Korteweg–de Vries equation ,Mathematics ,Mathematical physics ,Quantum anomalies ,010308 nuclear & particles physics ,Yang–Baxter equation ,Faddeev-Popov ghosts ,010102 general mathematics ,Algebraic Bethe ansatz ,Quantum dilogarithm ,Complete integrability ,Quantum inverse problem method - Abstract
International audience; This survey was written by students of L. D. Faddeev under the editorship of L. A. Takhtajan. Sections 1.1, 1.2, 2–4, and 6 were written by Takhtajan, §§1.3 and 1.4 by F. A. Smirnov, §§5.1 and 5.2 by E. K. Sklyanin, §§5.3–5.6 by Sklyanin, Smirnov, and Takhtajan, §7.1 by M. A. Semenov- Tian-Shansky, §§7.2–7.6 by Takhtajan and S. L. Shatashvili, §7.7 by A. Yu. Alekseev and Shatashvili, and §8 by I. Ya. Aref'eva.
- Published
- 2017
5. Научное наследие Л. Д. Фаддеева. Обзор работ
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Evgeny Sklyanin, F. Smirnov, Leon Armenovich Takhtadzhyan, Michael Semenov-Tian-Shansky, Anton Yur'evich Alekseev, Irina Yaroslavna Aref'eva, and Samson L. Shatashvili
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Physics ,010102 general mathematics ,0103 physical sciences ,0101 mathematics ,010306 general physics ,01 natural sciences - Published
- 2017
6. Coadjoint Orbits, Cocycles and Gravitational Wess–Zumino
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Anton Alekseev and Samson L. Shatashvili
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010308 nuclear & particles physics ,0103 physical sciences ,010306 general physics ,01 natural sciences - Published
- 2018
7. Coadjoint Orbits, Cocycles and Gravitational Wess–Zumino
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Samson L. Shatashvili, Anton Alekseev, Institut des Hautes Etudes Scientifiques (IHES), and IHES
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High Energy Physics - Theory ,Boundary (topology) ,FOS: Physical sciences ,01 natural sciences ,decoupling ,Quantization (physics) ,High Energy Physics::Theory ,Loop group ,0103 physical sciences ,010306 general physics ,Mathematical Physics ,orbit ,Mathematics ,Mathematical physics ,010308 nuclear & particles physics ,Group (mathematics) ,Wess–Zumino–Witten model ,Statistical and Nonlinear Physics ,Wess-Zumino term ,Term (logic) ,16. Peace & justice ,Action (physics) ,boundary condition ,High Energy Physics - Theory (hep-th) ,gravitation ,Wess-Zumino-Witten model ,Path integral formulation ,[PHYS.GRQC]Physics [physics]/General Relativity and Quantum Cosmology [gr-qc] ,quantization ,path integral - Abstract
About 30 years ago, in a joint work with L. Faddeev we introduced a geometric action on coadjoint orbits. This action, in particular, gives rise to a path integral formula for characters of the corresponding group $G$. In this paper, we revisit this topic and observe that the geometric action is a 1-cocycle for the loop group $LG$. In the case of $G$ being a central extension, we construct Wess-Zumino (WZ) type terms and show that the cocycle property of the geometric action gives rise to a Polyakov-Wiegmann (PW) formula. In particular, we obtain a PW type formula for the Polyakov's gravitational WZ action. After quantization, this formula leads to an interesting bulk-boundary decoupling phenomenon previously observed in the WZW model. We explain that this decoupling is a general feature of the Wess-Zumino terms obtained from geometric actions, and that in this case the path integral is expressed in terms of the 2-cocycle which defines the central extension. In memory of our teacher Ludwig Faddeev., Comment: 15 pages, v2: references added
- Published
- 2018
8. Quantum geometry and quiver gauge theories
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Vasily Pestun, Nikita Nekrasov, Samson L. Shatashvili, Institut des Hautes Etudes Scientifiques (IHES), IHES, and Institut des Hautes Etudes Scientifiques ( IHES )
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High Energy Physics - Theory ,dimension: 6 ,algebra: Kac-Moody ,Quantum affine algebra ,dimension: 5 ,algebra: affine ,[PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph] ,braid group ,algebra: Lie ,torus ,01 natural sciences ,K-theory ,monopole ,[ PHYS.HTHE ] Physics [physics]/High Energy Physics - Theory [hep-th] ,Mathematics - Algebraic Geometry ,High Energy Physics::Theory ,algebra: Hecke ,Mathematics - Quantum Algebra ,Gauge theory ,Mathematics::Representation Theory ,dimension: 2 ,Mathematical Physics ,Mathematical physics ,Chern-Simons term ,[PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th] ,Quiver ,supercharge ,compactification ,quantum algebra ,Yang-Baxter equation ,FOS: Physical sciences ,gauge field theory: supersymmetry ,0103 physical sciences ,quantum geometry ,FOS: Mathematics ,Quantum Algebra (math.QA) ,0101 mathematics ,Representation Theory (math.RT) ,moduli ,Algebraic Geometry (math.AG) ,R-matrix ,instanton: moduli space ,superpotential: twist ,010308 nuclear & particles physics ,Yang–Baxter equation ,010102 general mathematics ,Superpotential ,Quantum algebra ,Statistical and Nonlinear Physics ,gauge field theory: quiver ,High Energy Physics - Theory (hep-th) ,[ PHYS.MPHY ] Physics [physics]/Mathematical Physics [math-ph] ,Coulomb ,quantization ,Yangian ,Mathematics - Representation Theory - Abstract
We study macroscopically two dimensional $\mathcal{N}=(2,2)$ supersymmetric gauge theories constructed by compactifying the quiver gauge theories with eight supercharges on a product $\mathbb{T}^{d} \times \mathbb{R}^{2}_{\epsilon}$ of a $d$-dimensional torus and a two dimensional cigar with $\Omega$-deformation. We compute the universal part of the effective twisted superpotential. In doing so we establish the correspondence between the gauge theories, quantization of the moduli spaces of instantons on $\mathbb{R}^{2-d} \times \mathbb{T}^{2+d}$ and singular monopoles on $\mathbb{R}^{2-d} \times \mathbb{T}^{1+d}$, for $d=0,1,2$, and the Yangian $\mathbf{Y}_{\epsilon}(\mathfrak{g}_{\Gamma})$, quantum affine algebra $\mathbf{U}^{\mathrm{aff}}_q(\mathfrak{g}_{\Gamma})$, or the quantum elliptic algebra $\mathbf{U}^{\mathrm{ell}}_{q,p}(\mathfrak{g}_{\Gamma})$ associated to Kac-Moody algebra $\mathfrak{g}_{\Gamma}$ for quiver $\Gamma$., Comment: 83 pages
- Published
- 2018
9. Ludvig Dmitrievich Faddeev (on his 80th birthday)
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Vladimir E. Zakharov, Aleksei Borisovich Zhizhchenko, Samson L. Shatashvili, V. P. Maslov, P P Kulish, Valerii A. Rubakov, I. Ya. Aref'eva, V E Fortov, L.N. Lipatov, Alexander M. Polyakov, A. A. Slavnov, L. A. Takhtadzhyan, Michael Semenov-Tian-Shansky, Viktor Matveev, Serguei Vital'evich Kislyakov, Viktor M Buchstaber, Valerii Vasil'evich Kozlov, Il'dar Abdullovich Ibragimov, Yu. S. Osipov, Yu. A. Simonov, I. A. Sokolov, S. P. Novikov, Evgenii Pavlovich Velikhov, and Yakov G. Sinai
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General Mathematics ,Mathematics ,Mathematical physics - Published
- 2014
10. Darboux coordinates, Yang-Yang functional, and gauge theory
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Nikita Nekrasov, Samson L. Shatashvili, and A. A. Rosly
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High Energy Physics - Theory ,Nuclear and High Energy Physics ,Pure mathematics ,Instanton ,FOS: Physical sciences ,Darboux integral ,01 natural sciences ,Mathematics - Algebraic Geometry ,High Energy Physics::Theory ,symbols.namesake ,Conjugacy class ,Gauge group ,0103 physical sciences ,FOS: Mathematics ,Gauge theory ,010306 general physics ,Algebraic Geometry (math.AG) ,Mathematical Physics ,Mathematical physics ,Mathematics ,Physics ,010308 nuclear & particles physics ,Riemann surface ,Superpotential ,Mathematical analysis ,Statistical and Nonlinear Physics ,Atomic and Molecular Physics, and Optics ,Moduli space ,High Energy Physics - Theory (hep-th) ,Hitchin system ,Mathematics - Symplectic Geometry ,symbols ,Symplectic Geometry (math.SG) - Abstract
The moduli space of SL(2) flat connections on a punctured Riemann surface with the fixed conjugacy classes of the monodromies around the punctures is endowed with a system of holomorphic Darboux coordinates, in which the generating function of the variety of SL(2)-opers is identified with the universal part of the effective twisted superpotential of the corresponding four dimensional N=2 supersymmetric theory subject to the two-dimensional Omega-deformation. This allows to give a definition of the Yang-Yang functionals for the quantum Hitchin system in terms of the classical geometry of the moduli space of local systems for the dual gauge group, and connect it to the instanton counting of the four dimensional gauge theories, in the rank one case., 25 pages, 11 figures, v1. in the proceedings of Cargese conference "String Theory: Formal Developments and Applications" (Jun 21-Jul 3, 2010); reported also at six other conferences in 2010, v2. references corrected
- Published
- 2014
11. Quantum Integrability and Supersymmetric Vacua
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Nikita Nekrasov and Samson L. Shatashvili
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High Energy Physics - Theory ,Physics ,Ring (mathematics) ,Physics and Astronomy (miscellaneous) ,010308 nuclear & particles physics ,High Energy Physics::Phenomenology ,FOS: Physical sciences ,Supersymmetry ,01 natural sciences ,High Energy Physics - Theory (hep-th) ,Grassmannian ,0103 physical sciences ,Cotangent bundle ,Equivariant map ,Gauge theory ,010306 general physics ,Mathematics::Symplectic Geometry ,Quantum ,Mathematical physics ,Quantum cohomology - Abstract
This is an announcement of some of the results of a longer paper where the supersymmetric vacua of two dimensional N=2 susy gauge theories with matter are shown to be in one-to-one correspondence with the eigenstates of integrable spin chain Hamiltonians. The correspondence between the Heisenberg spin chain and the two dimensional U(N) theory with fundamental hypermultiplets is reviewed in detail. We demonstrate the isomorphism of the equivariant quantum cohomology of the cotangent bundle to the Grassmanian manifold Gr(N,L) and the ring of quantum integrals of motion of the length L SU(2) XXX spin chain, in the N-particle sector. This paper accompanies arXiv:0901.4744, Comment: 21 pp., short version II, conference in honour of T.Eguchi's 60th anniversary; v2. typos and refs corrected
- Published
- 2009
12. Higgs Bundles, Gauge Theories and Quantum Groups
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Samson L. Shatashvili and Anton A. Gerasimov
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High Energy Physics - Theory ,Physics ,FOS: Physical sciences ,Statistical and Nonlinear Physics ,Representation theory ,Moduli space ,Bethe ansatz ,High Energy Physics - Theory (hep-th) ,Higgs boson ,Equivariant map ,Geometric Langlands correspondence ,Gauge theory ,Wave function ,Mathematical Physics ,Mathematical physics - Abstract
The appearance of the Bethe Ansatz equation for the Nonlinear Schr\"{o}dinger equation in the equivariant integration over the moduli space of Higgs bundles is revisited. We argue that the wave functions of the corresponding two-dimensional topological U(N) gauge theory reproduce quantum wave functions of the Nonlinear Schr\"{o}dinger equation in the $N$-particle sector. This implies the full equivalence between the above gauge theory and the $N$-particle sub-sector of the quantum theory of Nonlinear Schr\"{o}dinger equation. This also implies the explicit correspondence between the gauge theory and the representation theory of degenerate double affine Hecke algebra. We propose similar construction based on the $G/G$ gauged WZW model leading to the representation theory of the double affine Hecke algebra. The relation with the Nahm transform and the geometric Langlands correspondence is briefly discussed., Comment: 48 pages, typos corrected, one reference added
- Published
- 2007
13. Bethe/Gauge correspondence on curved spaces
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Nikita Nekrasov and Samson L. Shatashvili
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Physics ,High Energy Physics - Theory ,Nuclear and High Energy Physics ,Conjecture ,Topological quantum field theory ,Integrable system ,High Energy Physics::Phenomenology ,FOS: Physical sciences ,Supersymmetry ,Invariant (physics) ,Bethe ansatz ,symbols.namesake ,High Energy Physics::Theory ,Mathematics - Algebraic Geometry ,High Energy Physics - Theory (hep-th) ,Poincaré conjecture ,FOS: Mathematics ,symbols ,Gauge theory ,Algebraic Geometry (math.AG) ,Mathematical physics - Abstract
Bethe/gauge correspondence identifies supersymmetric vacua of massive gauge theories invariant under the two dimensional $$ \mathcal{N} $$ = 2 Poincare supersymmetry with the stationary states of some quantum integrable system. The supersymmetric theory can be twisted in a number of ways, producing a topological field theory. For these theories we compute the handle gluing operator ℋ. We also discuss the Gaudin conjecture on the norm of Bethe states and its connection to ℋ.
- Published
- 2014
14. Closed strings from SO(8) Yang–Mills instantons
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Ruben Minasian, Samson L. Shatashvili, Pierre Vanhove, Centre de Physique Théorique [Palaiseau] (CPHT), École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS), Yale University [New Haven], Service de Physique Théorique (SPhT), and Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Centre National de la Recherche Scientifique (CNRS)
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High Energy Physics - Theory ,Heterotic string theory ,Physics ,Nuclear and High Energy Physics ,Instanton ,[PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th] ,Worldsheet ,SO(8) ,FOS: Physical sciences ,Yang–Mills existence and mass gap ,Supersymmetry ,Wedge (geometry) ,High Energy Physics::Theory ,High Energy Physics - Theory (hep-th) ,Tachyon ,Mathematical physics - Abstract
When eight-dimensional instantons, satisfying F \wedge F = \pm \star_8 (F\wedge F), shrink to zero size, we find stringy objects in higher order ten-dimensional Yang-Mills (viewed as a low-energy limit of open string theory). The associated F^4 action is a combination of two independent parts having a single-trace and a double-trace structure. As a result we get a D-string from the single-trace term and a fundamental string from the double-trace. The latter has (8,0) supersymmetry on the worldsheet and couplings to the background gauge fields of a heterotic string. A correlation between the conformal factor of the instanton and the tachyon field is conjectured., Comment: harvmac, v2: minor textual changes. To appear in Nucl. Phys. B
- Published
- 2001
15. An orbifold of Type 0B strings and non-supersymmetric gauge theories
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Samson L. Shatashvili, Igor R. Klebanov, and Nikita Nekrasov
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High Energy Physics - Theory ,Physics ,Nuclear and High Energy Physics ,010308 nuclear & particles physics ,Group (mathematics) ,Center (category theory) ,FOS: Physical sciences ,Type (model theory) ,16. Peace & justice ,String theory ,01 natural sciences ,Massless particle ,High Energy Physics::Theory ,Reflection (mathematics) ,High Energy Physics - Theory (hep-th) ,0103 physical sciences ,Gauge theory ,010306 general physics ,Orbifold ,Mathematical physics - Abstract
We study a ${{\IZ}}_2$ orbifold of Type 0B string theory by reflection of six of the coordinates (this theory may also be thought of as a ${{\IZ}}_4$ orbifold of Type IIB string theory by a rotation by $\pi$ in three independent planes). We show that the only massless mode localized on the fixed fourplane $\IR^{3,1}$ is a U(1) gauge field. After introducing D3-branes parallel to the fixed fourplane we find non-supersymmetric non-abelian gauge theories on their worldvolume. One of our results is that the theory on equal numbers of electric and magnetic D3-branes placed at the fourplane is the ${{\IZ}}_4$ orbifold of ${\cal N}=4$ supersymmetric Yang-Mills theory by the center of its R-symmetry group., Comment: 15 pages, harvmac; v2: very minor corrections; v3: a comment about pure glue theory added
- Published
- 2000
16. D -Particle Bound States and Generalized Instantons
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Nikita Nekrasov, Samson L. Shatashvili, and Gregory W. Moore
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High Energy Physics - Theory ,Physics ,Instanton ,Reduction (recursion theory) ,010308 nuclear & particles physics ,FOS: Physical sciences ,Statistical and Nonlinear Physics ,01 natural sciences ,High Energy Physics::Theory ,High Energy Physics - Theory (hep-th) ,Gauge group ,0103 physical sciences ,Bound state ,Particle ,010306 general physics ,Quantum ,Particle Physics - Theory ,Mathematical Physics ,Mathematical physics - Abstract
We compute the principal contribution to the index in the supersymmetric quantum mechanical systems which are obtained by reduction to 0+1 dimensions of $\mathcal{N}=1$, $D=4,6,10$ super-Yang-Mills theories with gauge group SU(N). The results are: ${1\over{N^{2}}}$ for $D=4,6$, $\sum_{d | N} {1\over{d^{2}}}$ for D=10. We also discuss the D=3 case., harvmac, 24 pages; v2. references added, typos corrected; v3. one more reference added
- Published
- 2000
17. Central extensions of gauge groups revisited
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Samson L. Shatashvili, Andrei Losev, Gregory W. Moore, and Nikita Nekrasov
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High Energy Physics - Theory ,Pure mathematics ,Group extension ,Group (mathematics) ,General Mathematics ,FOS: Physical sciences ,General Physics and Astronomy ,Lie group ,Vector bundle ,Automorphism ,Characteristic class ,Algebra ,Mathematics - Algebraic Geometry ,High Energy Physics - Theory (hep-th) ,Gauge group ,FOS: Mathematics ,Central charge ,Algebraic Geometry (math.AG) ,Mathematics - Abstract
We present an explicit construction for the central extension of the group $\Map(X, G)$ where $X$ is a compact manifold and $G$ is a Lie group. If $X$ is a complex curve we obtain a simple construction of the extension by the Picard variety $\Pic(X)$. The construction is easily adapted to the extension of $\Aut(E)$, the gauge group of automorphisms of a nontrivial vector bundle $E$., 7 pages, harvmac. References added
- Published
- 1998
18. Superstrings and manifolds of exceptional holonomy
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Samson L. Shatashvili and Cumrun Vafa
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Heterotic string theory ,Compactification (physics) ,General Mathematics ,Mathematical analysis ,Holonomy ,General Physics and Astronomy ,Superstring theory ,Supersymmetry ,Manifold ,Mathematics::Algebraic Geometry ,Operator algebra ,Mathematics::Differential Geometry ,Mirror symmetry ,Mathematical physics ,Mathematics - Abstract
The condition of having an $N=1$ spacetime supersymmetry for heterotic string leads to 4 distinct possibilities for compactifications namely compactifications down to 6,4,3 and 2 dimensions. Compactifications to 6 and 4 dimensions have been studied extensively before (corresponding to $K3$ and a Calabi-Yau threefold respectively). Here we complete the study of the other two cases corresponding to compactification down to 3 on a 7 dimensional manifold of $G_2$ holonomy and compactification down to 2 on an 8 dimensional manifold of $Spin(7)$ holonomy. We study the extended chiral algebra and find the space of exactly marginal deformations. It turns out that the role the $U(1)$ current plays in the $N=2$ superconformal theories, is played by tri-critical Ising model in the case of $G_2$ and Ising model in the case of $Spin(7)$ manifolds. Certain generalizations of mirror symmetry are found for these two cases. We also discuss a topological twisting in each case.
- Published
- 1995
19. Exceptional magic
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Samson L. Shatashvili and Cumrun Vafa
- Subjects
Nuclear and High Energy Physics ,Atomic and Molecular Physics, and Optics - Published
- 1995
20. QUANTIZATION OF INTEGRABLE SYSTEMS AND FOUR DIMENSIONAL GAUGE THEORIES
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Samson L. Shatashvili and Nikita Nekrasov
- Subjects
High Energy Physics - Theory ,Instanton ,FOS: Physical sciences ,01 natural sciences ,Mathematics - Algebraic Geometry ,High Energy Physics::Theory ,Quantization (physics) ,Mathematics - Analysis of PDEs ,0103 physical sciences ,FOS: Mathematics ,Gauge theory ,010306 general physics ,Algebraic Geometry (math.AG) ,Mathematical Physics ,Mathematical physics ,S-matrix ,Physics ,Nonlinear Sciences - Exactly Solvable and Integrable Systems ,010308 nuclear & particles physics ,High Energy Physics::Phenomenology ,Superpotential ,Mathematical Physics (math-ph) ,Nonlinear Sciences::Exactly Solvable and Integrable Systems ,High Energy Physics - Theory (hep-th) ,Hitchin system ,Supersymmetric gauge theory ,AGT correspondence ,Exactly Solvable and Integrable Systems (nlin.SI) ,Analysis of PDEs (math.AP) - Abstract
We study four dimensional N=2 supersymmetric gauge theory in the Omega-background with the two dimensional N=2 super-Poincare invariance. We explain how this gauge theory provides the quantization of the classical integrable system underlying the moduli space of vacua of the ordinary four dimensional N=2 theory. The epsilon-parameter of the Omega-background is identified with the Planck constant, the twisted chiral ring maps to quantum Hamiltonians, the supersymmetric vacua are identified with Bethe states of quantum integrable systems. This four dimensional gauge theory in its low energy description has two dimensional twisted superpotential which becomes the Yang-Yang function of the integrable system. We present the thermodynamic-Bethe-ansatz like formulae for these functions and for the spectra of commuting Hamiltonians following the direct computation in gauge theory. The general construction is illustrated at the examples of the many-body systems, such as the periodic Toda chain, the elliptic Calogero-Moser system, and their relativistic versions, for which we present a complete characterization of the L^2-spectrum. We very briefly discuss the quantization of Hitchin system., 32 pp. 1 figure
- Published
- 2010
21. Black hole physics and Liouville theory
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Samson L. Shatashvili and Emil J. Martinec
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Physics ,General Relativity and Quantum Cosmology ,Nuclear and High Energy Physics ,Scalar field theory ,Liouville function ,Gauge theory ,Liouville field theory ,String theory ,Scalar field ,Schwarzschild radius ,Relationship between string theory and quantum field theory ,Mathematical physics - Abstract
Hamiltonian path integral quantization of the SO(2, 1)/SO(2) and SO(2, 1)/SO(1, 1) gauged WZW models is considered. The SO(2, 1)/SO(2) model yields the Liouville theory coupled to a free scalar field theory after eliminating the group coordinates in favor of their conjugate momenta. The SO(2, 1)/SO(1, 1) model, recently argued to be a two-dimensional black-hole solution to string theory, can also be studied in momentum space. The resulting negative-metric Liouville-like theory has indefinite cosmological constant, is coupled to a positive-metric free scalar field, and lives on a Minkowski world sheet. The scaling variable |μ| of Liouville theory is related to the mass of the black hole. The connection to Liouville theory should provide the exact solution for correlation functions in the euclidean black-hole geometry using matrix models and Liouville theory; for the Lorentz-signature Schwarzschild geometry it gives us a tool to investigate the properties of singularities in string theory.
- Published
- 1992
22. Supersymmetric vacua and Bethe ansatz
- Author
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Samson L. Shatashvili and Nikita Nekrasov
- Subjects
High Energy Physics - Theory ,Physics ,Nuclear and High Energy Physics ,Spin group ,Hubbard model ,010308 nuclear & particles physics ,FOS: Physical sciences ,Supersymmetry ,01 natural sciences ,Atomic and Molecular Physics, and Optics ,Bethe ansatz ,High Energy Physics::Theory ,High Energy Physics - Theory (hep-th) ,0103 physical sciences ,Condensed Matter::Strongly Correlated Electrons ,Gauge theory ,Quantum field theory ,Yangian ,010306 general physics ,Mathematical physics ,Spin-½ - Abstract
An announcement of some results of a longer paper where the supersymmetric vacua of two dimensional N=2 susy gauge theories with matter are shown to be in one-to-one correspondence with the eigenstates of integrable spin chain Hamiltonians. The Heisenberg spin chain is mapped to the two dimensional U(N) theory with fundamental hypermultiplets, the XXZ spin chain is mapped to the analogous three dimensional super-Yang-Mills theory compactified on a circle, the XYZ spin chain and eight-vertex model are related to the four dimensional theory compactified on a torus. The correspondence extends to any spin group, representations, boundary conditions, and inhomogeneity, it includes Sinh-Gordon and non-linear Schroedinger models as well as the dynamical spin chains such as the Hubbard model. Compactifications of four dimensional N=2 theories on a two-sphere lead to the instanton-corrected Bethe equations. We propose a completely novel way for the Yangian, quantum affine, and elliptic algebras to act as a symmetry of a union of quantum field theories. This paper accompanies arXiv:0901.4748, Comment: 35 pages, short version I, Cargese and Landau-100 conferences proceedings; v2. typos and refs corrected
- Published
- 2009
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23. Quantum groups and WZNW models
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Samson L. Shatashvili and A. Alekseev
- Subjects
Sigma model ,Quantum group ,High Energy Physics::Lattice ,Current algebra ,Wess–Zumino–Witten model ,Lie group ,Statistical and Nonlinear Physics ,Symmetry group ,17B37 ,81R50 ,High Energy Physics::Theory ,Theoretical physics ,58F07 ,81T40 ,Quantum electrodynamics ,Quantum field theory ,Quantum ,Mathematical Physics ,Mathematics - Abstract
An explanation of the appearance of quantum groups in chiral WZNW models is given. Invariance of the theory under quantum group action is discussed.
- Published
- 1990
24. From geometric quantization to conformal field theory
- Author
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A. Alekseev and Samson L. Shatashvili
- Subjects
Physics ,Geometric quantization ,Primary field ,Group (mathematics) ,Conformal field theory ,Lie group ,Statistical and Nonlinear Physics ,81S10 ,Minimal models ,Type (model theory) ,Space (mathematics) ,Second quantization ,Interpretation (model theory) ,Algebra ,81R50 ,High Energy Physics::Theory ,Quantization (physics) ,58F06 ,81T40 ,Conformal symmetry ,Mathematics::Quantum Algebra ,17B81 ,Mathematical Physics ,Mathematical physics ,Mathematics - Abstract
Investigation of 2d conformal field theory in terms of geometric quantization is given. We quantize the so-called model space of the compact Lie group, Virasoro group and Kac-Moody group. In particular, we give a geometrical interpretation of the Virasoro discrete series and explain that this type of geometric quantization reproduces the chiral part of CFT (minimal models, 2d-gravity, WZNW theory). In the appendix we discuss the relation between classical (constant)r-matrices and this geometrical approach.
- Published
- 1990
25. On A Field Theory of Open Strings, Tachyon Condensation and Closed Strings
- Author
-
Samson L. Shatashvili
- Subjects
Physics ,High Energy Physics::Theory ,Theoretical physics ,Non-critical string theory ,Tachyon condensation ,Quantum electrodynamics ,Gauge theory ,String field theory ,Type I string theory ,Tachyonic field ,String (physics) ,Relationship between string theory and quantum field theory - Abstract
I review the physical properties of different vacua in the background independent open string field theory.
- Published
- 2007
26. Erratum To: Darboux coordinates, Yang-Yang functional, and gauge theory
- Author
-
Nikita Nekrasov, Samson L. Shatashvili, and A. A. Rosly
- Subjects
Statistical and Nonlinear Physics ,Gauge theory ,Action-angle coordinates ,Mathematical Physics ,Mathematics ,Mathematical physics - Published
- 2015
27. Factorization Conjecture and the Open/Closed String Correspondence
- Author
-
Samson L. Shatashvili, Ivo Sachs, and Marcus Baumgartl
- Subjects
Physics ,High Energy Physics - Theory ,Nuclear and High Energy Physics ,Pure mathematics ,Conjecture ,FOS: Physical sciences ,Boundary (topology) ,Conformal map ,Field (mathematics) ,String (physics) ,High Energy Physics::Theory ,High Energy Physics - Theory (hep-th) ,Factorization ,Path integral formulation ,Field theory (psychology) - Abstract
We present evidence for the factorization of the world-sheet path integrals for 2d conformal field theories on the disk into bulk and boundary contributions. This factorization is then used to reinterpret a shift in closed string backgrounds in terms of boundary deformations in background independent open string field theory. We give a proof of the factorization conjecture in the cases where the background is represented by WZW and related models., 21 pages
- Published
- 2004
28. On non-abelian structures in open string field theory
- Author
-
Samson L. Shatashvili and Anton A. Gerasimov
- Subjects
Physics ,High Energy Physics - Theory ,Nuclear and High Energy Physics ,Open string ,Degrees of freedom ,FOS: Physical sciences ,Space (mathematics) ,Differential operator ,Theoretical physics ,High Energy Physics - Theory (hep-th) ,Simple (abstract algebra) ,Field theory (psychology) ,Abelian group ,Algebra over a field - Abstract
Multi-brane backgrounds are studied in the framework of the background independent open string field theory. A simple description of the non-abelian degrees of freedom is given. Algebra of the differential operators acting on the space of functions on the space-time provides a natural tool for the discussion of this phenomena., 16 pages, harvmac b mode, references added
- Published
- 2001
29. On Unification of RR Couplings
- Author
-
Emil T. Akhmedov, Samson L. Shatashvili, and Anton A. Gerasimov
- Subjects
Physics ,High Energy Physics - Theory ,Nuclear and High Energy Physics ,Theoretical physics ,Overline ,Unification ,High Energy Physics - Theory (hep-th) ,Open string ,High Energy Physics::Phenomenology ,FOS: Physical sciences ,Algebra over a field ,Differential operator - Abstract
We consider the couplings of RR fields with open string sector for $Dp$-${\overline{Dp}}$ backgrounds of various $p$. Proposed approach, based on the approximation of the open string algebra by the algebra of differential operators, provides the unified description of these couplings and their interrelations., References added, Latex, 18 pages
- Published
- 2001
30. Stringy Higgs Mechanism and the Fate of Open Strings
- Author
-
Samson L. Shatashvili and Anton A. Gerasimov
- Subjects
Physics ,High Energy Physics - Theory ,Nuclear and High Energy Physics ,Conjecture ,Bosonic string theory ,Scalar (mathematics) ,High Energy Physics::Phenomenology ,FOS: Physical sciences ,String field theory ,symbols.namesake ,Theoretical physics ,High Energy Physics::Theory ,Tachyon ,High Energy Physics - Theory (hep-th) ,symbols ,Gauge theory ,Abelian group ,Higgs mechanism - Abstract
We propose a refinement of the physical picture describing different vacua in bosonic string theory. The vacua with closed strings and open strings are connected by the string field theory version of the Higgs mechanism, generalizing the Higgs mechanism of an abelian gauge field interacting with a complex scalar. In accordance with Sen's conjecture, the condensation of the tachyon is an essential part of the story. We consider this phenomenon from the point of view of both a world-sheet sigma-model and the target-space theory. In the Appendix the relevant remarks regarding the choice of the coordinates in the background independent open string field theory are given., 21pages, harvmac b mode, references added
- Published
- 2000
31. THE FRECKLED INSTANTONS
- Author
-
Samson L. Shatashvili, Nikita Nekrasov, and Andrei Losev
- Subjects
Physics ,Intersection theory ,medicine.medical_specialty ,Instanton ,Sigma model ,High Energy Physics::Lattice ,High Energy Physics::Phenomenology ,010102 general mathematics ,Field (mathematics) ,Renormalization group ,Space (mathematics) ,01 natural sciences ,Moduli space ,High Energy Physics::Theory ,Theoretical physics ,0103 physical sciences ,medicine ,010307 mathematical physics ,Gauge theory ,0101 mathematics - Abstract
We study instanton-corrected renormalization group flow in the two dimensional sigma models and four dimensional gauge theory. In two dimensions we do that by replacing the non-linear supersymmetric CP N −1 model by the gauged linear sigma model which is in the same universality class. We compare the moduli spaces of the instantons in the non-linear model and that of BPS field configurations in the linear model. We reduce the problem of matching of the parameters of the two systems to the intersection theory on the compact moduli space of the latter model. In four dimensions we find that the analogue of the linear sigma model is the gauge theory on the non-commutative space-time. Its BPS moduli space is the space of torsion free sheaves. Both cases (2d and 4d) are unified by the notion of the freckled instantons. We also put an end to the discussion of the nature of the superpotentials W ∼ σlogσ in 2d and 4d and discover the surprising disconnectnessness of the effective target space.
- Published
- 2000
32. On Exact Tachyon Potential in Open String Field Theory
- Author
-
Anton A. Gerasimov and Samson L. Shatashvili
- Subjects
High Energy Physics - Theory ,Physics ,Nuclear and High Energy Physics ,Change of variables ,Field (physics) ,Tachyon condensation ,Order (ring theory) ,FOS: Physical sciences ,Kinetic term ,Tree (descriptive set theory) ,High Energy Physics::Theory ,Tachyon ,High Energy Physics - Theory (hep-th) ,Field theory (psychology) ,Mathematics::Symplectic Geometry ,Mathematical physics - Abstract
In these notes we revisit the tachyon lagrangian in the open string field theory using background independent approach of Witten from 1992. We claim that the tree level lagrangian (up to second order in derivatives and modulo some class of field redefinitions) is given by $L = e^{-T} (\partial T)^2 + (1+T)e^{-T}$. Upon obvious change of variables this leads to the potential energy $-\phi^2 \log {\phi^2 \over e}$ with canonical kinetic term. This lagrangian may be also obtained from the effective tachyon lagrangian of the p-adic strings in the limit $p\to 1$. Applications to the problem of tachyon condensation are discussed., Comment: 12pages, harvmac b mode, corrected some typos
- Published
- 2000
- Full Text
- View/download PDF
33. Freckled Instantons in Two and Four Dimensions
- Author
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Nikita Nekrasov, Samson L. Shatashvili, and A. Losev
- Subjects
Physics ,High Energy Physics - Theory ,Theoretical physics ,Instanton ,Physics and Astronomy (miscellaneous) ,Compactification (physics) ,Sigma model ,High Energy Physics - Theory (hep-th) ,Supersymmetric gauge theory ,FOS: Physical sciences ,Gauge theory ,Topological defect - Abstract
Field theory with instantons can be partially regularized by adding degrees of freedom at some scale. These extra degrees of freedom lead to the appearence of the new topological defects. These defects which we call freckles have some characteristic size depending on the scale at which the extra degrees of freedom revive. The examples of two dimensional sigma model, four dimensional gauge theory are studied. The compactification of the four dimensional supersymmetric gauge theory down to two dimensions is also considered and the new phenomena are found., Latex, 10 pp., Talk by N.N. at Strings'99
- Published
- 1999
34. On Non-Supersymmetric CFT in Four Dimensions
- Author
-
Samson L. Shatashvili and Nikita Nekrasov
- Subjects
Physics ,High Energy Physics - Theory ,Class (set theory) ,Type 0 string theory ,General Physics and Astronomy ,FOS: Physical sciences ,Global symmetry ,Coupling (probability) ,High Energy Physics::Theory ,Amplitude ,Planar ,High Energy Physics - Theory (hep-th) ,Beta function (physics) ,Limit (mathematics) ,Mathematical physics - Abstract
We show that the $\mathcal{N}=0$ theories on the self-dual D3-branes of Type 0 string theory are in the class of the previously considered tadpole-free orbifolds of $\mathcal{N} = 4$ theory (although they have SO(6) global symmetry) and hence have vanishing beta function in the planar limit to all orders in 't Hooft coupling. Also, all planar amplitudes in this theory are equal to those of $\mathcal{N} = 4$ theory, up to a rescaling of the coupling., Comment: harvmac, 4 pp; v2. Z_4 field content corrected, references reworked
- Published
- 1999
- Full Text
- View/download PDF
35. Two-dimensional Conformal Field Theories on AdS_{2d+1} Backgrounds
- Author
-
Jan de Boer and Samson L. Shatashvili
- Subjects
High Energy Physics - Theory ,Physics ,Bosonization ,Nuclear and High Energy Physics ,Field (physics) ,010308 nuclear & particles physics ,Superstring theory ,FOS: Physical sciences ,Conformal map ,Space (mathematics) ,01 natural sciences ,3. Good health ,Theoretical physics ,High Energy Physics - Theory (hep-th) ,0103 physical sciences ,010306 general physics ,String duality ,Computer Science::Databases - Abstract
Various exact two-dimensional conformal field theories with AdS_{2d+1} target space are constructed. These models can be solved using bosonization techniques. Some examples are presented that can be used in building perturbative superstring theories with AdS backgrounds, including AdS_5., Comment: 36 pages, harvmac
- Published
- 1999
- Full Text
- View/download PDF
36. Duality from Topological Symmetry
- Author
-
Laurent Baulieu and Samson L. Shatashvili
- Subjects
High Energy Physics - Theory ,Physics ,Nuclear and High Energy Physics ,Unification ,Duality (optimization) ,FOS: Physical sciences ,Context (language use) ,Topology ,Dual (category theory) ,High Energy Physics::Theory ,High Energy Physics - Theory (hep-th) ,Dual polyhedron ,Gauge theory ,Abelian group ,Symmetry (geometry) ,Particle Physics - Theory - Abstract
We describe topological gauge theories for which duality properties are encoded by construction. We study them for compact manifolds of dimensions four, eight and two. The fields and their duals are treated symmetrically, within the context of field--antifield unification. Dual formulations correspond to different gauge-fixings of the topological symmetry. We also describe novel features in eight-dimensional theories, and speculate about their possible "Abelian" descriptions., Comment: 30 pages, harvmac file, references added
- Published
- 1998
- Full Text
- View/download PDF
37. M&m's
- Author
-
Andrei Losev, Gregory Moore, and Samson L. Shatashvili
- Subjects
High Energy Physics - Theory ,Nuclear and High Energy Physics - Abstract
We consider M theory 5-branes with compact transverse dimensions. In certain limits the theory on the 5-brane decouples and defines ``little string theories'' in 5+1 dimensions. We show that the familiar structure of IIA/IIB,M,F- theory in 10,11,12 dimensions respectively has a perfect parallel in a theory of strings and membranes in 6,7,8 dimensions. We call these theories $a/b,m,f$ theories. They have a coupling constant but no gravity. This construction clarifies some mysteries in F-theory and leads to several speculations about the phase structure of M theory., Comment: harvmac, 24 pages
- Published
- 1997
38. Integrating Over Higgs Branches
- Author
-
Samson L. Shatashvili, Gregory W. Moore, and Nikita Nekrasov
- Subjects
Large class ,Physics ,High Energy Physics - Theory ,Instanton ,Riemann surface ,FOS: Physical sciences ,Statistical and Nonlinear Physics ,Bethe ansatz ,Moduli space ,symbols.namesake ,High Energy Physics - Theory (hep-th) ,symbols ,Higgs boson ,Mathematics::Symplectic Geometry ,Mathematical Physics ,Schrödinger's cat ,Quotient ,Mathematical physics - Abstract
We develop some useful techinques for integrating over Higgs branches in supersymmetric theories with 4 and 8 supercharges. In particular, we define a regularized volume for hyperkahler quotients. We evaluate this volume for certain ALE and ALF spaces in terms of the hyperkahler periods. We also reduce these volumes for a large class of hyperkahler quotients to simpler integrals. These quotients include complex coadjoint orbits, instanton moduli spaces on R^4 and ALE manifolds, Hitchin spaces, and moduli spaces of parabolic Higgs bundles on Riemann surfaces. In the case of Hitchin spaces the evaluation of the volume reduces to a summation over solutions of Bethe Ansatz equations for the non-linear Schroedinger system. We discuss some applications of our results., Comment: 32pp. harvmac big mode; v.2 34pp. typos fixed, sections 4.1, 5.2 substantially improved
- Published
- 1997
- Full Text
- View/download PDF
39. Chiral Lagrangians, Anomalies, Supersymmetry, and Holomorphy
- Author
-
Nikita Nekrasov, Gregory W. Moore, Samson L. Shatashvili, and Andrei Losev
- Subjects
Physics ,High Energy Physics - Theory ,Nuclear and High Energy Physics ,Gravity (chemistry) ,Integrable system ,Holomorphic function ,FOS: Physical sciences ,Supersymmetry ,Gauge (firearms) ,String (physics) ,High Energy Physics::Theory ,High Energy Physics - Theory (hep-th) ,Algebraic number ,Mathematical physics - Abstract
We investigate higher-dimensional analogues of the $bc$ systems of 2D RCFT. When coupled to gauge fields and Beltrami differentials defining integrable holomorphic structures the $bc$ partition functions can be explicitly evaluated using anomalies and holomorphy. The resulting induced actions generalize the chiral algebras of 2D RCFT to $2n$ dimensions. Moreover, $bc$ systems in four and six dimensions are closely related to supersymmetric matter. In particular, we show that $d=4, \mathcal{N}=2$ hypermultiplets induce a theory of self-dual Yang-Mills fields coupled to self-dual gravity. In this way the $bc$ systems fermionize both the algebraic sector of the $WZW_4$ theory, as defined by Losev et. al., and the classical open $\mathcal{N}_{ws}=2$ string., Comment: 31 pp., Harvmac (b) mode
- Published
- 1996
- Full Text
- View/download PDF
40. Four-Dimensional Avatars of Two-Dimensional RCFT
- Author
-
Nikita Nekrasov, Andrei Losev, Samson L. Shatashvili, and Gregory W. Moore
- Subjects
Physics ,High Energy Physics - Theory ,Nuclear and High Energy Physics ,Pure mathematics ,Holomorphic function ,Current algebra ,Vector bundle ,FOS: Physical sciences ,Atomic and Molecular Physics, and Optics ,Moduli space ,Quantization (physics) ,Mathematics - Algebraic Geometry ,High Energy Physics - Theory (hep-th) ,Algebraic surface ,Vertex (curve) ,FOS: Mathematics ,Symmetry (geometry) ,Algebraic Geometry (math.AG) - Abstract
We investigate a 4D analog of 2D WZW theory. The theory turns out to have surprising finiteness properties and an infinite-dimensional current algebra symmetry. Some correlation functions are determined by this symmetry. One way to define the theory systematically proceeds by the quantization of moduli spaces of holomorphic vector bundles over algebraic surfaces. We outline how one can define vertex operators in the theory. Finally, we define four-dimensional ``conformal blocks'' and present an analog of the Verlinde formula., Comment: 28pp. harvmac l-mode, Talk presented at Strings 95 and at the Trieste Conference on S-Duality and Mirror Symmetry. References added, misprints corrected, improved discussion of the gauged action
- Published
- 1995
- Full Text
- View/download PDF
41. Correlation functions in the Itzykson-Zuber model
- Author
-
Samson L. Shatashvili
- Subjects
High Energy Physics - Theory ,Physics ,81T08 ,Pure mathematics ,FOS: Physical sciences ,Statistical and Nonlinear Physics ,Rational function ,Function (mathematics) ,Unitary matrix ,Measure (mathematics) ,81T27 ,Exponential function ,Linear differential equation ,High Energy Physics - Theory (hep-th) ,Simple (abstract algebra) ,Integral element ,Mathematical Physics - Abstract
The n-point function for the integral over unitary matrices with Itzykson-Zuber measure is reduced to the integral over Gelfand-Tzetlin table; integrand (for generic n) is given by linear exponential times rational function. For $n=2$ and in some cases for $n>2$ later in fact is the polinomial and this allows to give an explicit and simple expression for all 2-point and a set of n-point functions. For the most general n-point function a simple linear differential equation is constructed., 13p., corrected TEX version, Preprint IASSNS-HEP-92/61
- Published
- 1993
42. Comment on the Background Independent Open String Theory
- Author
-
Samson L. Shatashvili
- Subjects
High Energy Physics - Theory ,Physics ,Nuclear and High Energy Physics ,Theoretical physics ,High Energy Physics::Theory ,High Energy Physics - Theory (hep-th) ,Open string ,FOS: Physical sciences ,String field theory ,Action (physics) - Abstract
A direct derivation of the string field theory action in the Witten's background independent open string theory for the case when ghosts and matter are decoupled is given and consequences are discussed., Comment: 8p., harvmac
- Published
- 1993
- Full Text
- View/download PDF
43. Free Field Representation for the Classical Limit of Quantum Affine Algebra
- Author
-
Samson L. Shatashvili and Sergei L. Lukyanov
- Subjects
Physics ,High Energy Physics - Theory ,Nuclear and High Energy Physics ,Quantum affine algebra ,High Energy Physics::Theory ,Deformation (mechanics) ,High Energy Physics - Theory (hep-th) ,Simple (abstract algebra) ,FOS: Physical sciences ,Free field ,Representation (mathematics) ,Classical limit ,Mathematical physics - Abstract
Free field representation for the classical limit of quantum affine algebra is constructed by simple deformation of the known expressions from WZW theory., 7p, IASSNS-HEP-92/62, RU-92/37
- Published
- 1992
44. Generalized conifolds and four dimensional Script N = 1 superconformal theories
- Author
-
Steven S. Gubser, Samson L. Shatashvili, and Nikita Nekrasov
- Subjects
Physics ,Nuclear and High Energy Physics ,Conifold ,Supergravity ,Field (mathematics) ,Fixed point ,String theory ,High Energy Physics::Theory ,Singularity ,Gravitational singularity ,ADE classification ,Mathematics::Symplectic Geometry ,Particle Physics - Theory ,Mathematical physics - Abstract
We consider D3-branes placed at singularities of Calabi-Yau threefolds which generalize the conifold singularity and have an ADE classification. The $\CN=1$ superconformal theories dictating their low-energy dynamics are infrared fixed points arising from deforming the corresponding ADE $\CN=2$ superconformal field theories by mass terms for adjoint chiral fields. We probe the geometry by a single $D3$-brane and discuss the near-horizon supergravity solution for a large number $N$ of coincident $D3$-branes. This paper lays groundwork for the detailed study of the non-trivial renormalization group flow connecting supersymmetric fixed points in four dimensions using string theory on AdS spaces. Specifically, we consider D3-branes placed at singularities of Calabi-Yau threefolds which generalize the conifold singularity and have an ADE classification. The $\mathcal{N}=1$ superconformal theories dictating their low-energy dynamics are infrared fixed points arising from deforming the corresponding ADE $\mathcal{N}=2$ superconformal field theories by mass terms for adjoint chiral fields. We probe the geometry with a single $D3$-brane and discuss the near-horizon supergravity solution for a large number $N$ of coincident $D3$-branes.
- Published
- 1999
45. Path integral quantization of the coadjoint orbits of the virasoro group and 2-d gravity
- Author
-
A. Alekseev and Samson L. Shatashvili
- Subjects
Gravitation ,Physics ,High Energy Physics::Theory ,Nuclear and High Energy Physics ,Quantization (physics) ,Quantum electrodynamics ,Path integral formulation ,Virasoro algebra ,Quantum gravity ,Quantum field theory ,Kac–Moody algebra ,Wess–Zumino model ,Mathematical physics - Abstract
Geometrical interpretation of the appearance of SL(2, R ) symmetry in the 2-d quantum gravity is given in terms of the theory of the coadjoint orbits of the Virasoro group. Equivalence of the 2-d gravity and the special type of gauged SL(2, R ) WZNW theory is shown.
- Published
- 1989
46. Algebraic and Hamiltonian methods in the theory of non-Abelian anomalies
- Author
-
Samson L. Shatashvili and L. D. Faddeev
- Subjects
Introduction to gauge theory ,Statistical and Nonlinear Physics ,Yang–Mills theory ,BRST quantization ,symbols.namesake ,Hamiltonian lattice gauge theory ,symbols ,Algebraic number ,Abelian group ,Hamiltonian (quantum mechanics) ,Mathematical Physics ,Group theory ,Mathematical physics ,Mathematics - Published
- 1984
47. Quantization of symplectic orbits of compact Lie groups by means of the functional integral
- Author
-
Samson L. Shatashvili, L. D. Faddeev, and A. Alekseev
- Subjects
Classical group ,Pure mathematics ,Symplectic group ,Spin group ,Simple Lie group ,Mathematical analysis ,General Physics and Astronomy ,Lie group ,Unitary group ,Maximal torus ,Geometry and Topology ,Moment map ,Mathematical Physics ,Mathematics - Abstract
The functional integral for the quantization of the coadjoint orbits of the unitary and orthogonal groups is given by means of an explicit construction of the corresponding ≪Darboux≫ variables.
- Published
- 1988
48. String operator formalism and functional integral in the holomorphic representation
- Author
-
A. Losev, Samson L. Shatashvili, A. Yu. Morozov, and A. A. Roslyi
- Subjects
Physics ,Formalism (philosophy of mathematics) ,Theoretical computer science ,Holomorphic function ,Statistical and Nonlinear Physics ,Mathematical Physics ,Mathematical physics - Published
- 1989
49. Realization of the Schwinger term in the Gauss law and the possibility of correct quantization of a theory with anomalies
- Author
-
Samson L. Shatashvili and L. D. Faddeev
- Subjects
Physics ,Geometric quantization ,Nuclear and High Energy Physics ,Gauss's law for gravity ,Canonical quantization ,High Energy Physics::Lattice ,Quantization (physics) ,symbols.namesake ,Regularization (physics) ,Path integral formulation ,symbols ,Gauss's law ,Quantum field theory ,Mathematical physics - Abstract
The explicit regularization of the Weyl fermion current leading to the anomalous commutation relation of the Gauss law constraint is established. This requires the modification of the canonical quantization of the corresponding gauge model. The modified form of functional integral quantization for this model is proposed.
- Published
- 1986
50. PROPAGATOR FOR THE RELATIVISTIC SPINNING PARTICLE VIA FUNCTIONAL INTEGRAL OVER TRAJECTORIES
- Author
-
A. Yu. Alekseev and Samson L. Shatashvili
- Subjects
Physics ,Nuclear and High Energy Physics ,Angular momentum ,General Physics and Astronomy ,Propagator ,Lie group ,Astronomy and Astrophysics ,Symmetry group ,Space (mathematics) ,Classical mechanics ,Path integral formulation ,Condensed Matter::Strongly Correlated Electrons ,Orbit (control theory) ,Spin-½ - Abstract
A spin factor is defined by means of the canonical 2-form on the coadjoint orbit of the SO (d+1) group. Including this spin factor in the definition of the path integral leads to the correct propagator for a system of arbitrary spin in a space of dimension d.
- Published
- 1988
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