28 results on '"Mauricio Romo"'
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2. Exponential BPS Graphs and D Brane Counting on Toric Calabi-Yau Threefolds: Part I
- Author
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Pietro Longhi, Sibasish Banerjee, and Mauricio Romo
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High Energy Physics - Theory ,Physics ,Pure mathematics ,Conifold ,010308 nuclear & particles physics ,010102 general mathematics ,Quiver ,FOS: Physical sciences ,Statistical and Nonlinear Physics ,01 natural sciences ,Exponential function ,High Energy Physics::Theory ,Mathematics - Algebraic Geometry ,Mathematics::Algebraic Geometry ,High Energy Physics - Theory (hep-th) ,Physics::Plasma Physics ,0103 physical sciences ,FOS: Mathematics ,Calabi–Yau manifold ,D-brane ,0101 mathematics ,Brane ,Algebraic Geometry (math.AG) ,Mathematics::Symplectic Geometry ,Mathematical Physics - Abstract
We study BPS spectra of D-branes on local Calabi-Yau threefolds O(-p)circle plus O(p-2) -> P-1 with p = 0,1, corresponding to C-3/Z(2) and the resolved conifold. Nonabelianization for exponential networks is applied to compute directly unframed BPS indices counting states with D2 and D0 brane charges. Known results on these BPS spectra are correctly reproduced by computing new types of BPS invariants of 3d-5d BPS states, encoded by nonabelianization, through their wall-crossing. We also develop the notion of exponential BPS graphs for the simplest toric examples, and show that they encode both the quiver and the potential associated to the Calabi-Yau via geometric engineering., Communications in Mathematical Physics, 388, ISSN:1432-0916, ISSN:0010-3616
- Published
- 2021
3. Hybrid models for homological projective duals and noncommutative resolutions
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Jirui Guo and Mauricio Romo
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High Energy Physics - Theory ,Mathematics - Algebraic Geometry ,High Energy Physics - Theory (hep-th) ,FOS: Mathematics ,FOS: Physical sciences ,Statistical and Nonlinear Physics ,Algebraic Geometry (math.AG) ,Mathematical Physics - Abstract
We study hybrid models arising as homological projective duals (HPD) of certain projective embeddings $f:X\rightarrow\mathbb{P}(V)$ of Fano manifolds $X$. More precisely, the category of B-branes of such hybrid models corresponds to the HPD category of the embedding $f$. B-branes on these hybrid models can be seen as global matrix factorizations over some compact space $B$ or, equivalently, as the derived category of the sheaf of $\mathcal{A}$-modules on $B$, where $\mathcal{A}$ is an $A_{\infty}$ algebra. This latter interpretation corresponds to a noncommutative resolution of $B$. We compute explicitly the algebra $\mathcal{A}$ by several methods, for some specific class of hybrid models, and find that in general it takes the form of a smash product of an $A_{\infty}$ algebra with a cyclic group. Then we apply our results to the HPD of $f$ corresponding to a Veronese embedding of projective space and the projective embedding of Fano complete intersections in $\mathbb{P}^{n}$., Comment: 50 pages, LaTeX; v3: references added, several improvements on the examples and the section on complete intersections. Published version
- Published
- 2022
4. A-branes, foliations and localization
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Sibasish Banerjee, Pietro Longhi, and Mauricio Romo
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High Energy Physics - Theory ,Nuclear and High Energy Physics ,FOS: Physical sciences ,Statistical and Nonlinear Physics ,High Energy Physics::Theory ,Mathematics - Algebraic Geometry ,Mathematics::Algebraic Geometry ,High Energy Physics - Theory (hep-th) ,Mathematics - Symplectic Geometry ,FOS: Mathematics ,Symplectic Geometry (math.SG) ,Algebraic Geometry (math.AG) ,Mathematics::Symplectic Geometry ,Mathematical Physics - Abstract
This paper studies a notion of enumerative invariants for stable $A$-branes, and discusses its relation to invariants defined by spectral and exponential networks. A natural definition of stable $A$-branes and their counts is provided by the string theoretic origin of the topological $A$-model. This is the Witten index of the supersymmetric quantum mechanics of a single $D3$ brane supported on a special Lagrangian in a Calabi-Yau threefold. Geometrically, this is closely related to the Euler characteristic of the $A$-brane moduli space. Using the natural torus action on this moduli space, we reduce the computation of its Euler characteristic to a count of fixed points via equivariant localization. Studying the $A$-branes that correspond to fixed points, we make contact with definitions of spectral and exponential networks. We find agreement between the counts defined via the Witten index, and the BPS invariants defined by networks. By extension, our definition also matches with Donaldson-Thomas invariants of $B$-branes related by homological mirror symmetry., 51 pages
- Published
- 2022
5. Aspects of $(2,2)$ and $(0,2)$ hybrid models
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Mauricio Romo and Marco Bertolini
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High Energy Physics - Theory ,Heterotic string theory ,Instanton ,Algebra and Number Theory ,Spacetime ,Worldsheet ,Superpotential ,Yukawa potential ,Linear model ,FOS: Physical sciences ,General Physics and Astronomy ,Range (mathematics) ,Theoretical physics ,High Energy Physics - Theory (hep-th) ,Mathematical Physics ,Mathematics - Abstract
In this work we study the topological rings of two dimensional (2,2) and (0,2) hybrid models. In particular, we use localization to derive a formula for the correlators in both cases, focusing on the B- and B/2-twists. Although our methods apply to a vast range of hybrid CFTs, we focus on hybrid models suitable for compactifications of the heterotic string. In this case, our formula provides unnormalized Yukawa couplings of the spacetime superpotential. We apply our techniques to hybrid phases of linear models, and we find complete agreement with known results in other phases. We also obtain a prediction for a certain class of correlators involving twisted operators in (2,2) Landau-Ginzburg orbifolds. For (0,2) theories, our argument does not rely on the existence of a (2,2) locus. Finally, we derive vanishing conditions concerning worldsheet instanton corrections in (0,2) B/2-twisted hybrid models., 63 pages
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- 2020
6. D-brane central charge and Landau-Ginzburg orbifolds
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Johanna Knapp, Mauricio Romo, and Emanuel Scheidegger
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Physics ,High Energy Physics - Theory ,Partition function (quantum field theory) ,Sigma model ,010102 general mathematics ,Complex system ,FOS: Physical sciences ,Statistical and Nonlinear Physics ,01 natural sciences ,Moduli space ,Mathematics - Algebraic Geometry ,High Energy Physics - Theory (hep-th) ,0103 physical sciences ,FOS: Mathematics ,010307 mathematical physics ,D-brane ,0101 mathematics ,Central charge ,Algebraic Geometry (math.AG) ,Mathematics::Symplectic Geometry ,Mathematical Physics ,Mathematical physics - Abstract
We propose a formula for the exact central charge of a B-type D-brane that is expected to hold in all regions of the Kahler moduli space of a Calabi-Yau. For Landau-Ginzburg orbifolds we propose explicit expressions for the mathematical objects that enter into the central charge formula. We show that our results are consistent with results in FJRW theory and the hemisphere partition function of the gauged linear sigma model., 91 pages, 2 figures, typos corrected, references added. Published version
- Published
- 2020
7. A GLSM view on Homological Projective Duality
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Zhuo Chen, Jirui Guo, and Mauricio Romo
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High Energy Physics - Theory ,Mathematics - Algebraic Geometry ,Mathematics::Algebraic Geometry ,High Energy Physics - Theory (hep-th) ,FOS: Mathematics ,FOS: Physical sciences ,Statistical and Nonlinear Physics ,Algebraic Geometry (math.AG) ,Mathematical Physics - Abstract
Given a gauged linear sigma model (GLSM) $\mathcal{T}_{X}$ realizing a projective variety $X$ in one of its phases, i.e. its quantum K\"ahler moduli has a maximally unipotent point, we propose an \emph{extended} GLSM $\mathcal{T}_{\mathcal{X}}$ realizing the homological projective dual category $\mathcal{C}$ to $D^{b}Coh(X)$ as the category of B-branes of the Higgs branch of one of its phases. In most of the cases, the models $\mathcal{T}_{X}$ and $\mathcal{T}_{\mathcal{X}}$ are anomalous and the analysis of their Coulomb and mixed Coulomb-Higgs branches gives information on the semiorthogonal/Lefschetz decompositions of $\mathcal{C}$ and $D^{b}Coh(X)$. We also study the models $\mathcal{T}_{X_{L}}$ and $\mathcal{T}_{\mathcal{X}_{L}}$ that correspond to homological projective duality of linear sections $X_{L}$ of $X$. This explains why, in many cases, two phases of a GLSM are related by homological projective duality. We study mostly abelian examples: linear and Veronese embeddings of $\mathbb{P}^{n}$ and Fano complete intersections in $\mathbb{P}^{n}$. In such cases, we are able to reproduce known results as well as produce some new conjectures. In addition, we comment on the construction of the HPD to a nonabelian GLSM for the Pl\"ucker embedding of the Grassmannian $G(k,N)$., Comment: 53 pages, LaTeX; v2: published version, updated references, corrected typos
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- 2020
- Full Text
- View/download PDF
8. All-Order Volume Conjecture for Closed 3-Manifolds from Complex Chern–Simons Theory
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Mauricio Romo, Dongmin Gang, and Masahito Yamazaki
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High Energy Physics - Theory ,Root of unity ,Chern–Simons theory ,FOS: Physical sciences ,Volume conjecture ,01 natural sciences ,Mathematics - Geometric Topology ,Mathematics - Quantum Algebra ,0103 physical sciences ,FOS: Mathematics ,Quantum Algebra (math.QA) ,Limit (mathematics) ,0101 mathematics ,Connection (algebraic framework) ,Mathematical Physics ,Mathematical physics ,Physics ,Conjecture ,010308 nuclear & particles physics ,010102 general mathematics ,Order (ring theory) ,Geometric Topology (math.GT) ,Statistical and Nonlinear Physics ,Mathematical Physics (math-ph) ,Partition function (mathematics) ,Mathematics::Geometric Topology ,High Energy Physics - Theory (hep-th) - Abstract
We propose an extension of the recently-proposed volume conjecture for closed hyperbolic 3-manifolds, to all orders in perturbative expansion. We first derive formulas for the perturbative expansion of the partition function of complex Chern-Simons theory around a hyperbolic flat connection, which produces infinitely-many perturbative invariants of the closed oriented 3-manifold. The conjecture is that this expansion coincides with the perturbative expansion of the Witten-Reshetikhin-Turaev invariants at roots of unity $q=e^{2 \pi i/r}$ with $r$ odd, in the limit $r \to \infty$. We provide numerical evidence for our conjecture., Comment: 22 pages, 2 figures; v2: published version
- Published
- 2018
9. Beijing lectures on the grade restriction rule
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Kentaro Hori, Johanna Knapp, Richard Eager, and Mauricio Romo
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Partition function (quantum field theory) ,Sigma model ,010308 nuclear & particles physics ,Applied Mathematics ,General Mathematics ,010102 general mathematics ,01 natural sciences ,Algebra ,Mathematics::Algebraic Geometry ,Beijing ,Gauge group ,0103 physical sciences ,0101 mathematics ,Mathematics::Symplectic Geometry ,Mathematics - Abstract
The authors describe the relationships between categories of B-branes in different phases of the non-Abelian gauged linear sigma model. The relationship is described explicitly for the model proposed by Hori and Tong with non-Abelian gauge group that connects two non-birational Calabi-Yau varieties studied by Rodland. A grade restriction rule for this model is derived using the hemisphere partition function and it is used to map B-type D-branes between the two Calabi-Yau varieties.
- Published
- 2017
10. Cluster partition function and invariants of 3-manifolds
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Mauricio Romo
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High Energy Physics - Theory ,Discrete mathematics ,Knot complement ,Partition function (quantum field theory) ,Relation (database) ,010308 nuclear & particles physics ,Applied Mathematics ,General Mathematics ,010102 general mathematics ,FOS: Physical sciences ,Mathematical Physics (math-ph) ,String theory ,01 natural sciences ,Cluster algebra ,High Energy Physics::Theory ,High Energy Physics - Theory (hep-th) ,Gauge group ,0103 physical sciences ,Path integral formulation ,Cluster (physics) ,0101 mathematics ,Mathematical Physics ,Mathematics - Abstract
We review some recent developments in Chern-Simons theory on a hyperbolic 3-manifold $M$ with complex gauge group $G$. We focus on the case $G=SL(N,\mathbb{C})$ and with $M$ a knot complement. The main result presented in this note is the cluster partition function, a computational tool that uses cluster algebra techniques to evaluate the Chern-Simons path integral. We also review various applications and open questions regarding the cluster partition function and some of its relation with string theory., Comment: 26 pages, 1 figure, contribution to the proceedings of the workshop "Non-abelian Gauged Linear Sigma Model and Geometric Representation Theory" held at BICMR (Jun. 2015). To appear in a special issue of Chinese Annals of Mathematics, Series B; v2: reference added
- Published
- 2017
11. Hemisphere partition function and analytic continuation to the conifold point
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Johanna Knapp, Emanuel Scheidegger, and Mauricio Romo
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High Energy Physics - Theory ,Pure mathematics ,Partition function (quantum field theory) ,Algebra and Number Theory ,Conifold ,010308 nuclear & particles physics ,Analytic continuation ,FOS: Physical sciences ,General Physics and Astronomy ,Singular point of a curve ,01 natural sciences ,Moduli space ,Quintic function ,Mathematics - Algebraic Geometry ,Mathematics::Algebraic Geometry ,Hypersurface ,High Energy Physics - Theory (hep-th) ,Quartic function ,0103 physical sciences ,FOS: Mathematics ,010306 general physics ,Algebraic Geometry (math.AG) ,Mathematics::Symplectic Geometry ,Mathematical Physics ,Mathematics - Abstract
We show that the hemisphere partition function for certain U(1) gauged linear sigma models (GLSMs) with D-branes is related to a particular set of Mellin-Barnes integrals which can be used for analytic continuation to the singular point in the K\"ahler moduli space of an $h^{1,1}=1$ Calabi-Yau (CY) projective hypersurface. We directly compute the analytic continuation of the full quantum corrected central charge of a basis of geometric D-branes from the large volume to the singular point. In the mirror language this amounts to compute the analytic continuation of a basis of periods on the mirror CY to the conifold point. However, all calculations are done in the GLSM and we do not have to refer to the mirror CY. We apply our methods explicitly to the cubic, quartic and quintic CY hypersurfaces., Comment: 65 pages
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- 2017
12. Notes on the Hemisphere
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Kentaro Hori and Mauricio Romo
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14J33 ,18E30 ,81T45 ,supersymmetric localization ,primitive forms ,53D45 ,53D37 ,Theoretical physics ,Matrix (mathematics) ,High Energy Physics::Theory ,81T40 ,boundary conditions ,81T60 ,Gromov-Witten theory ,Gauge theory ,Quantum field theory ,Supersymmetric quantum field theory ,Physics ,Partition function (quantum field theory) ,14D05 ,High Energy Physics::Phenomenology ,flat structure ,Superstring theory ,Supersymmetry ,Topological string theory ,81T13 ,32S40 ,gauged linear sigma models ,D-brane central charge ,81T30 ,Central charge ,14N35 - Abstract
In these notes, we provide an introduction to the hemisphere partition function of 2d $(2,2)$ supersymmetric gauge theories, and discuss its relation to the "D-brane central charge" which were studied in superstring theory, in 2d supersymmetric quantum field theory, and in topological string theory. We also discuss relation to "macroscopic loop" in matrix models. They are mostly reviews of the work by the authors, but contains some new results such as the partition function for a rotated supersymmetry as well as the differential equations.
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- 2019
13. Two-Sphere Partition Functions and Gromov–Witten Invariants
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Joshua M. Lapan, Hans Jockers, Mauricio Romo, David R. Morrison, and Vijay Kumar
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Mathematical analysis ,Statistical and Nonlinear Physics ,Pfaffian ,Codimension ,Partition function (mathematics) ,String theory ,Moduli space ,Moduli ,High Energy Physics::Theory ,Mathematics::Algebraic Geometry ,Mathematics::Differential Geometry ,Gauge theory ,Mirror symmetry ,Mathematics::Symplectic Geometry ,Mathematical Physics ,Mathematics ,Mathematical physics - Abstract
Many N = (2,2) two-dimensional nonlinear sigma models with Calabi-Yau target spaces admit ultraviolet descriptions as N = (2,2) gauge theories (gauged linear sigma models). We conjecture that the two-sphere partition function of such ultraviolet gauge theories — recently computed via localization by Benini et al. and Doroud et al. — yields the exact Kahler potential on the quantum Kahler moduli space for Calabi-Yau threefold target spaces. In particular, this allows one to compute the genus zero Gromov-Witten invariants for any such Calabi-Yau threefold without the use of mirror symmetry. More generally, when the infrared superconformal fixed point is used to compactify string theory, this provides a direct method to compute the spacetime Kahler potential of certain moduli (e.g., vector multiplet moduli in type IIA), exactly in α ' . We compute these quantities for the quintic and for Rodland's Pfaffian Calabi-Yau threefold and find agreement with existing results in the literature. We then apply our methods to a codimension four determinantal Calabi-Yau threefold in P 7 , recently given a nonabelian gauge theory description by the present authors, for which no mirror Calabi-Yau is currently known. We derive predictions for its Gromov-Witten invariants and verify that our predictions satisfy nontrivial geometric checks.
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- 2014
14. Aspects of defects in 3d-3d correspondence
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Mauricio Romo, Masahito Yamazaki, Dongmin Gang, and Nakwoo Kim
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High Energy Physics - Theory ,Physics ,Nuclear and High Energy Physics ,Compactification (physics) ,010308 nuclear & particles physics ,Supergravity ,FOS: Physical sciences ,Geometric Topology (math.GT) ,Supersymmetry ,01 natural sciences ,Cluster algebra ,Combinatorics ,Mathematics - Geometric Topology ,High Energy Physics - Theory (hep-th) ,Gauge group ,Mathematics - Quantum Algebra ,0103 physical sciences ,FOS: Mathematics ,Quantum Algebra (math.QA) ,010306 general physics ,General expression - Abstract
In this paper we study supersymmetric co-dimension 2 and 4 defects in the compactification of the 6d $(2,0)$ theory of type $A_{N-1}$ on a 3-manifold $M$. The so-called 3d-3d correspondence is a relation between complexified Chern-Simons theory (with gauge group $SL(N, \mathbb{C})$) on $M$ and a 3d $\mathcal{N}=2$ theory $T_{N}[M]$. We establish a dictionary for this correspondence in the presence of supersymmetric defects, which are knots/links inside the 3-manifold. Our study employs a number of different methods: state-integral models for complex Chern-Simons theory, cluster algebra techniques, domain wall theory $T[SU(N)]$, 5d $\mathcal{N}=2$ SYM, and also supergravity analysis through holography. These methods are complementary and we find agreement between them. In some cases the results lead to highly non-trivial predictions on the partition function. Our discussion includes a general expression for the cluster partition function, in particular for non-maximal punctures and $N>2$. We also highlight the non-Abelian description of the 3d $\mathcal{N}=2$ $T_N[M]$ theory with defect included, as well as its Higgsing prescription and the resulting `refinement' in complex CS theory. This paper is a companion to our shorter paper arXiv:1510.03884, which summarizes our main results., 129 pages (sorry), 22 figures
- Published
- 2016
15. Taming Supersymmetric Defects in 3d-3d Correspondence
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Dongmin Gang, Masahito Yamazaki, Nakwoo Kim, and Mauricio Romo
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Statistics and Probability ,High Energy Physics - Theory ,Relation (database) ,FOS: Physical sciences ,General Physics and Astronomy ,Context (language use) ,01 natural sciences ,Theoretical physics ,High Energy Physics::Theory ,Mathematics - Geometric Topology ,Gauge group ,0103 physical sciences ,Mathematics - Quantum Algebra ,FOS: Mathematics ,Quantum Algebra (math.QA) ,010306 general physics ,Mathematical Physics ,Physics ,Compactification (physics) ,010308 nuclear & particles physics ,Geometric Topology (math.GT) ,Statistical and Nonlinear Physics ,Partition function (mathematics) ,Dual (category theory) ,High Energy Physics - Theory (hep-th) ,Modeling and Simulation - Abstract
We study knots in 3d Chern-Simons theory with complex gauge group $SL(N,\mathbb{C})$, in the context of its relation with 3d $\mathcal{N}=2$ theory (the so-called 3d-3d correspondence). The defect has either co-dimension 2 or co-dimension 4 inside the 6d $(2,0)$ theory, which is compactified on a 3-manifold $\hat{M}$. We identify such defects in various corners of the 3d-3d correspondence, namely in 3d $SL(N,\mathbb{C})$ Chern-Simons theory, in 3d $\mathcal{N}=2$ theory, in 5d $\mathcal{N}=2$ super Yang-Mills theory, and in the M-theory holographic dual. We can make quantitative checks of the 3d-3d correspondence by computing partition functions at each of these theories. This Letter is a companion to a longer paper, which contains more details and more results., 6 pages, 3 figures
- Published
- 2015
16. Aspects of ABJM orbifolds
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Mauricio Romo and David Berenstein
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High Energy Physics - Theory ,Group (mathematics) ,General Mathematics ,Mathematical analysis ,Quiver ,Magnetic monopole ,FOS: Physical sciences ,General Physics and Astronomy ,Semiclassical physics ,Representation theory ,Moduli space ,High Energy Physics::Theory ,Theoretical physics ,High Energy Physics - Theory (hep-th) ,Brane ,Orbifold ,Mathematics - Abstract
We study abelian and non-abelian orbifolds of the ABJM model. We compute the precise moduli space of these models by analyzing the classical BPS equations for the theory on the cylinder, which include classical solutions of magnetic monopole operators. These determine the chiral ring of the theory, and thus they provide the complete set of order parameters determining the classical vacua of the theory. We show that the proper quantization of these semiclassical solutions gives us the topology of moduli space, including the additional quotient information due to the Chern-Simons levels. In general, we find that in the dual M-theory setup, the M-theory fiber is divided by the product of the Chern-Simons level times the order of the orbifold group, even in the non-abelian case. This depends non-trivially on how the different Chern-Simons terms have different levels in these constructions. We also see a direct relation in this setup between the Chern-Simons levels of the different groups and fluxes for fractional brane cycles. We also show that the problem of the moduli space can be much more easily analyzed by using the method of images and representation theory of crossed product algebras rather than dealing only with the quiver theory data., 52 pages, 6 figures. v2: reference added
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- 2010
17. Nonabelian 2D Gauge Theories for Determinantal Calabi-Yau Varieties
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David R. Morrison, Vijay Kumar, Mauricio Romo, Joshua M. Lapan, and Hans Jockers
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High Energy Physics - Theory ,Nuclear and High Energy Physics ,Sigma model ,FOS: Physical sciences ,Type (model theory) ,String theory ,01 natural sciences ,String (physics) ,Theoretical physics ,High Energy Physics::Theory ,Mathematics - Algebraic Geometry ,Mathematics::Algebraic Geometry ,0103 physical sciences ,FOS: Mathematics ,Calabi–Yau manifold ,Gauge theory ,0101 mathematics ,Abelian group ,Algebraic Geometry (math.AG) ,Mathematics::Symplectic Geometry ,Physics ,010308 nuclear & particles physics ,010102 general mathematics ,Moduli space ,High Energy Physics - Theory (hep-th) ,Mathematics::Differential Geometry - Abstract
The two-dimensional supersymmetric gauged linear sigma model (GLSM) with abelian gauge groups and matter fields has provided many insights into string theory on Calabi--Yau manifolds of a certain type: complete intersections in toric varieties. In this paper, we consider two GLSM constructions with nonabelian gauge groups and charged matter whose infrared CFTs correspond to string propagation on determinantal Calabi-Yau varieties, furnishing another broad class of Calabi-Yau geometries in addition to complete intersections. We show that these two models -- which we refer to as the PAX and the PAXY model -- are dual descriptions of the same low-energy physics. Using GLSM techniques, we determine the quantum K\"ahler moduli space of these varieties and find no disagreement with existing results in the literature., Comment: v3: 46 pages, 1 figure. Corrected phase structure of general linear determinantal varieties. Typos corrected
- Published
- 2012
18. Monopole operators, moduli spaces and dualities
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David Berenstein and Mauricio Romo
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High Energy Physics - Theory ,Physics ,Nuclear and High Energy Physics ,Supergravity ,Magnetic monopole ,Holomorphic function ,FOS: Physical sciences ,Semiclassical physics ,Supersymmetry ,Moduli space ,High Energy Physics::Theory ,symbols.namesake ,Theoretical physics ,High Energy Physics - Theory (hep-th) ,symbols ,Change of basis ,Hilbert–Poincaré series - Abstract
We develop semiclassical methods to analyze the spectrum of BPS monopole operators for superconformal field theories in three dimensions with N=2 supersymmetry. We show that the chiral ring of the theory results from the semiclassical holomorphic quantization of the solution of classical BPS equations of motion on the cylinder. We apply this formalism to various theories. We also use these techniques to compare the chiral rings of theories that might be related to each other via Seiberg dualities in four dimensions. We find that the change of basis transformations that generate dualities in four dimensions (homological operations) generically do not work in three dimensions in the presence of Chern-Simons terms. Instead, new theories generally arise this way. When dualities are possible, the Chern-Simons couplings need to satisfy certain arithmetic congruences. We also determine the spectrum of R-charges of the chiral ring operators by assembling them on a Hilbert series and by minimizing the coefficient of the maximum pole relative to the trial R-charge. This is related to volume minimization in theories with dual supergravity setups., Comment: 49 pages, 8 figures, JHEP format. v2: References added. A new subsection with quantum corrections to monopole operators is included. These quantum corrections restore some of the Seiberg dualities that did not match with the classical computation alone. Minor fix on one figure
- Published
- 2012
19. Unitary Chern-Simons matrix model and the Villain lattice action
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Miguel Tierz and Mauricio Romo
- Subjects
Physics ,Coupling constant ,High Energy Physics - Theory ,Nuclear and High Energy Physics ,Logarithm ,010308 nuclear & particles physics ,High Energy Physics::Lattice ,High Energy Physics - Lattice (hep-lat) ,Chern–Simons theory ,FOS: Physical sciences ,Unitary matrix ,16. Peace & justice ,01 natural sciences ,Unitary state ,Hermitian matrix ,High Energy Physics::Theory ,High Energy Physics - Lattice ,High Energy Physics - Theory (hep-th) ,Lattice (order) ,0103 physical sciences ,010306 general physics ,Heat kernel ,Mathematical physics - Abstract
We use the Villain approximation to show that the Gross-Witten model, in the weak- and strong-coupling limits, is related to the unitary matrix model that describes U(N) Chern-Simons theory on S^3. The weak-coupling limit corresponds to the q->1 limit of the Chern-Simons theory while the strong-coupling regime is related to the q->0 limit. In the latter case, there is a logarithmic relationship between the respective coupling constants. We also show how the Chern-Simons matrix model arises by considering two-dimensional Yang-Mills theory with the Villain action. This leads to a U(1)^N theory which is the Abelianization of 2d Yang-Mills theory with the heat-kernel lattice action. In addition, we show that the character expansion of the Villain lattice action gives the q deformation of the heat kernel as it appears in q-deformed 2d Yang-Mills theory. We also study the relationship between the unitary and Hermitian Chern-Simons matrix models and the rotation of the integration contour in the corresponding integrals., 17 pages, Minor corrections to match the published version
- Published
- 2011
20. SUSY Enhancements in (0,4) Deformations of AdS_3/CFT_2
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Mauricio Romo, Joshua M. Lapan, and Stéphane Detournay
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High Energy Physics - Theory ,Physics ,Nuclear and High Energy Physics ,Spacetime ,010308 nuclear & particles physics ,Worldsheet ,Supergravity ,FOS: Physical sciences ,Supersymmetry ,Deformation (meteorology) ,String theory ,01 natural sciences ,Symmetry (physics) ,High Energy Physics::Theory ,High Energy Physics - Theory (hep-th) ,0103 physical sciences ,Affine transformation ,010306 general physics ,Mathematical physics - Abstract
We discuss a marginal deformation of the SL(2,R) x SU(2) x U(1)^4 WZW model, which describes string theory on AdS_3 x S^3 x T^4, that corresponds to warping the S^3 factor. This deformation breaks part of the N=(4,4) supersymmetry of the undeformed dual CFT to N=(0,4) supersymmetry. In the spirit of work by Giveon, Kutasov, and Seiberg, we construct the asymptotic spacetime symmetry algebra from worldsheet operators and find a restoration of (4,4) supersymmetry at discrete values of the deformation parameter. We explain this result from various perspectives: the worldsheet, supergravity, and from the singular D1-D5 CFT. The supergravity analysis includes an asymptotic symmetry computation of the level of the affine SU(2) R-symmetry, which arises purely from B-field contributions., Comment: 16 pages; v2: references added
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- 2011
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21. Aspects of ABJM orbifolds with discrete torsion
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Mauricio Romo
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Physics ,High Energy Physics - Theory ,Nuclear and High Energy Physics ,Pure mathematics ,Crossed product ,High Energy Physics - Theory (hep-th) ,Torsion (algebra) ,FOS: Physical sciences ,Abelian group ,Twist ,Quotient ,Moduli space - Abstract
We analyze orbifolds with discrete torsion of the ABJM theory by a finite subgroup $\Gamma$ of $SU(2)\times SU(2)$ . Discrete torsion is implemented by twisting the crossed product algebra resulting after orbifolding. It is shown that, in general, the order $m$ of the cocycle we chose to twist the algebra by enters in a non trivial way in the moduli space. To be precise, the M-theory fiber is multiplied by a factor of $m$ in addition to the other effects that were found before in the literature. Therefore we got a $\mathbb{Z}_{\frac{k|\Gamma|}{m}}$ action on the fiber. We present a general analysis on how this quotient arises along with a detailed analysis of the cases where $\Gamma$ is abelian.
- Published
- 2010
22. String Theory on Warped AdS_3 and Virasoro Resonances
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Dan Israel, Mauricio Romo, Joshua M. Lapan, and Stéphane Detournay
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High Energy Physics - Theory ,Physics ,Nuclear and High Energy Physics ,010308 nuclear & particles physics ,Worldsheet ,Supergravity ,FOS: Physical sciences ,Supersymmetry ,String theory ,01 natural sciences ,Moduli space ,Theoretical physics ,High Energy Physics::Theory ,High Energy Physics - Theory (hep-th) ,0103 physical sciences ,Virasoro algebra ,Symmetry (geometry) ,010306 general physics ,Central charge - Abstract
We investigate aspects of holographic duals to time-like warped AdS_3 space-times--which include G\"odel's universe--in string theory. Using worldsheet techniques similar to those that have been applied to AdS_3 backgrounds, we are able to identify space-time symmetry algebras that act on the dual boundary theory. In particular, we always find at least one Virasoro algebra with computable central charge. Interestingly, there exists a dense set of points in the moduli space of these models in which there is actually a second commuting Virasoro algebra, typically with different central charge than the first. We analyze the supersymmetry of the backgrounds, finding related enhancements, and comment on possible interpretations of these results. We also perform an asymptotic symmetry analysis at the level of supergravity, providing additional support for the worldsheet analysis., Comment: 24 pages + appendices
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- 2010
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23. Supersymmetric Gödel and warped black holes in string theory
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Geoffrey Compère, Mauricio Romo, and Stéphane Detournay
- Subjects
High Energy Physics - Theory ,Physics ,Nuclear and High Energy Physics ,Particle physics ,Astrophysics::High Energy Astrophysical Phenomena ,Supergravity ,Fuzzball ,String theory ,Black hole ,General Relativity and Quantum Cosmology ,High Energy Physics::Theory ,Micro black hole ,Extremal black hole ,Black brane ,Black hole thermodynamics ,Mathematical physics - Abstract
It is observed that three-dimensional G\"odel black holes can be promoted to exact string theory backgrounds through an orbifold of an hyperbolic asymmetric marginal deformation of the SL(2,R) WZW model. Tachyons are found in the spectrum of long strings. Uplifting these solutions in type IIB supergravity, extremal black holes are shown to preserve one supersymmetry in accordance with the BTZ limit. We also make connections with some recently discussed warped black hole solutions of topologically massive gravity, showing that they actually correspond to quotients of spacelike squashed AdS_3., Comment: 15 pages
- Published
- 2008
24. Local supersymmetric extensions of the poincare and ads invariant gravity
- Author
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Mauricio Romo and Mokhtar Hassaine
- Subjects
High Energy Physics - Theory ,Physics ,Nuclear and High Energy Physics ,Spinor ,FOS: Physical sciences ,Invariant (physics) ,Gravitation ,MAJORANA ,High Energy Physics::Theory ,High Energy Physics - Theory (hep-th) ,Supersymmetric gauge theory ,Gauge theory ,Algebraic number ,Gauge symmetry ,Mathematical physics - Abstract
In all the odd dimensions which allow Majorana spinors, we consider a gravitational Lagrangian possessing local Poincare invariance and given by the dimensional continuation of the Euler density in one dimension less. We show that the local supersymmetric extension of this Lagrangian requires the algebra to be the maximal extension of the N=1 super-Poincare algebra. By maximal, we mean that in the right hand side of the anticommutator of the Majorana super charge appear all the possible central charges. The resulting action defines a Chern-Simons gauge theory for the maximal extension of the super-Poincare algebra. In these dimensions, we address the same problem for the AdS invariant gravity and we derive its supersymmetric extension for the minimal super-AdS algebra. The connection between both models is realized at the algebraic level through an expansion of their corresponding Lie super algebras. Within a procedure consistent with the expansion of the algebras, the local supersymmetric extension of the Poincare invariant gravity Lagrangian is derived from the super AdS one., Comment: 9 pages. Minor changes (typos and references added). Accepted in JHEP
- Published
- 2008
25. Compactification in first order gravity
- Author
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Mauricio Romo, Nelson Zamorano, and Rodrigo Aros
- Subjects
Physics ,High Energy Physics - Theory ,History ,Formalism (philosophy of mathematics) ,General Relativity and Quantum Cosmology ,Compactification (physics) ,High Energy Physics - Theory (hep-th) ,FOS: Physical sciences ,First order ,Computer Science Applications ,Education ,Mathematical physics - Abstract
The Kaluza-Klein compactification process is applied in five dimensions to CS gravity, for the anti-de Sitter and Poincar\'e groups, using the first order formalism. In this context some solutions are found and analyzed. Also, the conserved charges associated to the solutions are computed., Comment: Minor corrections
- Published
- 2007
26. Conformal Gravity from AdS/CFT mechanism
- Author
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Rodrigo Aros, Mauricio Romo, and Nelson Zamorano
- Subjects
Physics ,High Energy Physics - Theory ,Nuclear and High Energy Physics ,Hořava–Lifshitz gravity ,FOS: Physical sciences ,symbols.namesake ,AdS/CFT correspondence ,General Relativity and Quantum Cosmology ,High Energy Physics - Theory (hep-th) ,Conformal symmetry ,symbols ,Quantum gravity ,f(R) gravity ,Semiclassical gravity ,Higher-dimensional Einstein gravity ,Mathematical physics ,Induced gravity - Abstract
We explicitly calculate the induced gravity theory at the boundary of an asymptotically Anti-de Sitter five dimensional Einstein gravity. We also display the action that encodes the dynamics of radial diffeomorphisms. It is found that the induced theory is a four dimensional conformal gravity plus a scalar field. This calculation confirms some previous results found by a different approach., Revtex 8 pages, To be published in Phys. Rev. D
- Published
- 2006
27. Drift of particles in self-similar systems and its liouvillian interpretation
- Author
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Thomas Gilbert, Felipe Barra, and Mauricio Romo
- Subjects
Constant velocity ,Lorentz transformation ,Spectral properties ,FOS: Physical sciences ,Nonlinear Sciences - Chaotic Dynamics ,Graph ,symbols.namesake ,Resonance spectrum ,Classical mechanics ,Master equation ,symbols ,Statistical physics ,Chaotic Dynamics (nlin.CD) ,Dynamical billiards ,Eigenvalues and eigenvectors ,Mathematics - Abstract
We study the dynamics of classical particles in different classes of spatially extended self-similar systems, consisting of (i) a self-similar Lorentz billiard channel, (ii) a self-similar graph, and (iii) a master equation. In all three systems the particles typically drift at constant velocity and spread ballistically. These transport properties are analyzed in terms of the spectral properties of the operator evolving the probability densities. For systems (i) and (ii), we explain the drift from the properties of the Pollicott-Ruelle resonance spectrum and corresponding eigenvectors, To appear in Phys. Rev. E
- Published
- 2006
28. Taming supersymmetric defects in 3d–3d correspondence.
- Author
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Dongmin Gang, Nakwoo Kim, Mauricio Romo, and Masahito Yamazaki
- Subjects
SUPERSYMMETRY ,KNOT theory ,THREE-dimensional modeling ,GAUGE field theory ,YANG-Mills theory - Abstract
We study knots in 3d Chern–Simons theory with complex gauge group , in the context of its relation with 3d theory (the so-called 3d–3d correspondence). The defect has either co-dimension 2 or co-dimension 4 inside the 6d theory, which is compactified on a 3-manifold . We identify such defects in various corners of the 3d–3d correspondence, namely in 3d CS theory, in 3d theory, in 5d super Yang–Mills theory, and in the M-theory holographic dual. We can make quantitative checks of the 3d–3d correspondence by computing partition functions at each of these theories. This Letter is a companion to a longer paper [1], which contains more details and more results. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
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