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In this paper we extend the classical BV framework to gauge theories on spacetime manifolds with boundary. In particular, we connect the BV construction in the bulk with the BFV construction on the boundary and we develop its extension to strata of higher codimension in the case of manifolds with corners. We present several examples including electrodynamics, Yang-Mills theory and topological field theories coming from the AKSZ construction, in particular, the Chern-Simons theory, the BF theory, and the Poisson sigma model. This paper is the first step towards developing the perturbative quantization of such theories on manifolds with boundary in a way consistent with gluing. [ABSTRACT FROM AUTHOR]

In this paper, we prove a convergence theorem for sequences of Einstein Yang-Mills systems on U(1)-bundles over closed n-manifolds with some bounds for volumes, diameters, L2-norms of bundle curvatures, and L n2 -norms of curvature tensors. This result is a generalization of earlier compactness theorems for Einstein manifolds. [ABSTRACT FROM AUTHOR]

According to the standard cosmological model, thermodynamic conditions of the early Universe were such that nuclear matter existed in the state of quark–gluon plasma, rather than hadrons. On the other hand, it is generally believed that quantum gravity effects become ever more stronger as we approach the Big Bang, in particular, we expect that the phenomenon of space–time noncommutativity will be significant. Thus we are led to consider the properties of quarks and gluons in noncommutative space–time. For this, we employ the S O (2 , 3) ⋆ model of noncommutative gravity. As a first step towards the full theoretical treatment of the effects of noncommutativity on quark–gluon plasma, our main goal in this paper is to consistently incorporate Yang–Mills gauge fields in the S O (2 , 3) ⋆ framework and investigate their coupling to gravity that arises due to space–time noncommutativity. We construct an action that is invariant under deformed S O (2 , 3) ⋆ × S U (N) ⋆ gauge transformations and expand it perturbatively in orders of the canonical deformation parameter 𝜃 α β via Seiberg–Witten map. In particular, we analyze the flat-space–time limit and demonstrate that residual noncommutativity induces various new couplings of quarks and gluons. [ABSTRACT FROM AUTHOR]

In this paper, we review Schwinger’s formulation of Quantum Mechanics and argue that the mathematical structure behind Schwinger’s “Symbolism of Atomic Measurements” is that of a groupoid. In this framework, both the Hilbert space (Schrödinger picture) and the C∗-algebra (Heisenberg picture) of the system turn out to be derived concepts, that is, they arise from the underlying groupoid structure. [ABSTRACT FROM AUTHOR]

The entropic force experienced by a moving quarkonia in a plasma is computed in a hyperscaling violation background by holography approach. In that case, the axis of the moving quarkonia has an arbitrary angle with wind. We use the results for HSV parameters, which are obtained in our paper,1 as appropriate values satisfying condition ImVQQ̄<0. We will show that, in this background, the entropic force of the meson shows a decreasing behavior corresponding to increasing dissociation length. Results of this paper are in agreement with our mentioned work. In addition, we will find diffusion constant in an exact case and by an exact approach2 which satisfies the mentioned condition in there. [ABSTRACT FROM AUTHOR]

This paper deals with the massive three-dimensional Dirac operator coupled with a Lorentz scalar shell interaction supported on a compact smooth surface. The rigorous definition of the operator involves suitable transmission conditions along the surface. After showing the self-adjointness of the resulting operator, we switch to the investigation of its spectral properties, in particular, to the existence and non-existence of eigenvalues. In the case of an attractive coupling, we study the eigenvalue asymptotics as the mass becomes large and show that the behavior of the individual eigenvalues and their total number are governed by an effective Schrödinger operator on the boundary with an external Yang–Mills potential and a curvature-induced potential. [ABSTRACT FROM AUTHOR]

In this paper, the monopoles which are topological solitons in three space dimensions of k-field theories is studied. It is explicitly constructed that the magnetic monopoles arising in the recent study of Casana, Ferreira, and Hora of a generalized Yang–Mills–Higgs model which is controlled by the special positive function f. Using a variational method, we prove the existence of the finite-energy monopoles solution in the non-Abelian gauge field is proven. In particular, it is shown that, under the condition of the special weight function f, the finite-energy solution must be Bogomolnyi–Prasad–Sommerfield solution. [ABSTRACT FROM AUTHOR]

In this paper we present a new identity to associate the conservation laws of stress–energy tensor with the field equations in Yang–Mills theory. The Lorentz force is included with a consistent formulation as in Maxwell theory. [ABSTRACT FROM AUTHOR]

We demonstrate that the known expressions for the thermal partition function of large N Chern-Simons matter theories admit a simple Hilbert space interpretation as the partition function of an associated ungauged large N matter theory with one additional condition: the Fock space of this associated theory is projected down to the subspace of its quantum singlets i.e. singlets under the Gauss law for Chern-Simons gauge theory. Via the Chern-Simons / WZW correspondence, the space of quantum singlets are equivalent to the space of WZW conformal blocks. One step in our demonstration involves recasting the Verlinde formula for the dimension of the space of conformal blocks in SU(N)k and U(N)k,k′ WZW theories into a simple and physically transparent form, which we also rederive by evaluating the partition function and superconformal index of pure Chern-Simons theory in the presence of Wilson lines. A particular consequence of the projection of the Fock space of Chern-Simons matter theories to quantum (or WZW) singlets is the 'Bosonic Exclusion Principle': the number of bosons occupying any single particle state is bounded above by the Chern-Simons level. The quantum singlet condition (unlike its Yang-Mills Gauss Law counterpart) has a nontrivial impact on thermodynamics even in the infinite volume limit. In this limit the projected Fock space partition function reduces to a product of partition functions, one for each single particle state. These single particle state partition functions are q-deformations of their free boson and free fermion counterparts and interpolate between these two special cases. We also propose a formula for the large N partition function that is valid for arbitrary finite volume of the spatial S2 and not only at large volume. [ABSTRACT FROM AUTHOR]

With the goal of building a concrete co-dimension one holographically dual field theory for four dimensional asymptotically flat spacetimes (4d AFS) as a limit of AdS4/CFT3, we begin an investigation of 3d Chern-Simons matter (CSM) theories in the Carroll regime. We perform a Carroll (speed of light c → 0) expansion of the relativistic Chern-Simons action coupled to a massless scalar and obtain Carrollian CSM theories, which we show are invariant under the infinite dimensional 3d conformal Carroll or 4d Bondi-van der Burg-Metzner-Sachs (BMS4) symmetries, thus making them putative duals for 4d AFS. Concentrating on the leading-order electric Carroll CSM theory, we perform a null reduction of the 3d theory. Null reduction is a procedure to obtain non-relativistic theories from a higher dimensional relativistic theory. Curiously, null reduction of a Carrollian theory yields a relativistic lower-dimensional theory. We work with SU(N) × SU(M) CS theory coupled to bi-fundamental matter and show that when N = M, we obtain (rather surprisingly) a 2d Euclidean Yang-Mills theory after null reduction. We also comment on the reduction when N ≠ M and possible connections of the null-reduced Carroll theory to a candidate 2d Celestial CFT. [ABSTRACT FROM AUTHOR]

In this paper, we consider the case where electrons, magnetic monopoles and dyons become massless. Here, we consider the supersymmetric Yang-Mills (SYM) theories with classical gauge groups with a rank r, SU(r+1), SO(2r), Sp(2r) and SO(2r+1) which are studied by Riemann surfaces called Seiberg-Witten curves. We discuss physical singularity associated with massless particles, which can be studied by geometric singularity of vanishing 1-cycles in Riemann surfaces in hyperelliptic form. We pay particular attention to the cases where mutually nonlocal states become massless (Argyres-Douglas theories), which corresponds to Riemann surfaces degenerating into cusps. We discuss nontrivial topology on the moduli space of the theory, which is reflected as monodromy associated to vanishing 1-cycles. We observe how dyon charges get changed as we move around and through singularity in moduli space. [ABSTRACT FROM AUTHOR]

In this paper the Seiberg-Witten map is first analyzed for non-commutative Yang-Mills theories with the related methods, developed in the literature, for its explicit construction, that hold for any gauge group. These are exploited to write down the second-order Seiberg-Witten map for pure gravity with a constant non-commutativity tensor. In the analysis of pure gravity when the classical space-time solves the vacuum Einstein equations, we find for three distinct vacuum solutions that the corresponding non-commutative field equations do not have solution to first order in non-commutativity, when the Seiberg-Witten map is eventually inserted. In the attempt of understanding whether or not this is a peculiar property of gravity, in the second part of the paper, the Seiberg-Witten map is considered in the simpler case of Maxwell theory in vacuum in the absence of charges and currents. Once more, no obvious solution of the non-commutative field equations is found, unless the electromagnetic potential depends in a very special way on the wave vector. [ABSTRACT FROM AUTHOR]

In this paper, we use the Morse theory of the Yang–Mills–Higgs functional on the singular space of Higgs bundles on Riemann surfaces to compute the equivariant cohomology of the space of semistable U(2, 1)- and SU(2, 1)-Higgs bundles with fixed Toledo invariant. In the non-coprime case, this gives new results about the topology of the U(2, 1) and SU(2, 1) character varieties of surface groups. The main results are a calculation of the equivariant Poincaré polynomials, a Kirwan surjectivity theorem in the non-fixed determinant case, and a description of the action of the Torelli group on the equivariant cohomology of the character variety. This builds on earlier work for stable pairs and rank 2 Higgs bundles. [ABSTRACT FROM AUTHOR]

In this paper, we complete the proof of the existence of multiple solutions (and, in particular, non minimal ones), to the [variant_greek_epsilon]-Dirichlet problem obtained as a variational problem for the SU(2)[variant_greek_epsilon]-Yang-Mills functional. This is equivalent to proving the existence of multiple solutions to the Dirichlet problem for the SU(2)-Yang-Mills functional with small boundary data. In the first paper of this series this non-compact variational problem is transformed into the finite-dimensional problem of finding the critical points of the function J[variant_greek_epsilon](q), which is essentially the Yang-Mills functional evaluated on the approximate solutions, constructed via a gluing technique. In the present paper, we establish a Morse theory for J[variant_greek_epsilon](q), by means of Ljusternik-Schnirelmann theory, thus complete the proofs of Theorems 1-3 given by Isobe and Marini ['Small coupling limit and multiple solutions to the Dirichlet Problem for Yang-Mills connections in 4 dimensions - Part I,' J. Math. Phys. 53, 063706 (2012)]. [ABSTRACT FROM AUTHOR]

In this paper, we consider a model of interacting phantom and Yang-Mills (YM) fields by assuming dilaton-type coupling. Using the specific solution for YM equation previously found by the author, we obtain simple exact solutions for the accelerated expansion of the Friedmann-Robertson-Walker (FRW) cosmological model. Besides, we derive induced potentials of phantom field corresponding to some given regimes of expansion. The effective equations of state (EoS) have been reconstructed for all types of models considered here. [ABSTRACT FROM AUTHOR]

What is the real nature of pulsars? This is essentially a question of the fundamental strong interaction between quarks at low-energy scale and hence of the non-perturbative quantum chromo-dynamics, the solution of which would certainly be meaningful for us to understand one of the seven millennium prize problems (i.e., "Yang-Mills Theory") named by the Clay Mathematical Institute. After a historical note, it is argued here that a pulsar is very similar to an extremely big nucleus, but is a little bit different from the gigantic nucleus speculated 80 years ago by L. Landau. The paper demonstrates the similarity between pulsars and gigantic nuclei from both points of view: the different manifestations of compact stars and the general behavior of the strong interaction. [ABSTRACT FROM AUTHOR]

This paper deals in the thermodynamic properties of Einstein-Gauss-Bonnet and Einstein-Yang-Mills-Gauss-Bonnet black holes. It exhibits the various stable and unstable phases of the black holes in these two modified gravity theories. In the first section, that reveals the various aspects of Einstein-Gauss-Bonnet black holes, we chose to study the changes in the Hawking Temperature with variations in the radius of event horizon ( r) and charge ( Q); and tried to justify them physically. Secondly in case of Einstein-Yang-Mills-Gauss-Bonnet black holes, we have attempted to compare the changes in the various thermodynamic parameters with varying r and Q; with the Einstein-Gauss-Bonnet black holes at a macroscopic level. Here we have considered the Yang Mills tensor, electromagnetic Lagrangian added to the action integrand. Again this very work deals in drawing out the similarities between these two types of black holes, thereby throwing some light on the aspect of black hole stability. Later we have also introspected the effects of the Gauss-Bonnet coupling parameter α, whose function (6 αr), is added as a correction term to the black hole entropy. We have especially focused on what changes does it have upon the nature of the plots as to whether it enhances or reduces the effect of Q on the behavior of the curves. Finally this paper has also kept an eye at estimating the stability domains of the black holes described in these two gravity theories. [ABSTRACT FROM AUTHOR]

We present a renormalizability proof for spontaneously broken SU(2) gauge theory based on flow equations. It is a conceptually and technically simplified version of the earlier paper [5] including some extensions. The proof of [5] was also incomplete since an important assumption made implicitly in the proof of Lemma 2 there was not verified. So the present paper is also a corrected version of [5]. [ABSTRACT FROM AUTHOR]

In this paper we analyze the existence of the periodic orbits of the static, spherically symmetric Einstein–Yang–Mills Equations by using the qualitative theory of the ordinary differential equation. We prove that there are no periodic orbits restricted to some invariant set of codimension 1. Furthermore if there is a periodic orbit out of this invariant set, then there must be other periodic orbits, which are symmetric to the first one. We also have results on the non–existence of periodic orbits when the cosmological constant is negative. [ABSTRACT FROM AUTHOR]

We introduce and study the four-dimensional analogue of a mass generation mechanism for non-Abelian gauge fields suggested in the paper, Phys. Lett. B403, 297 (1997), in the case of three-dimensional space–time. The construction of the corresponding quantized theory is based on the fact that some nonlocal actions may generate local expressions for Green functions. An example of such a theory is the ordinary Yang–Mills field where the contribution of the Faddeev–Popov determinant to the Green functions can be made local by introducing additional ghost fields. We show that the quantized Hamiltonian for our theory unitarily acts in a Hilbert space of states and prove that the theory is renormalizable to all orders of perturbation theory. One-loop coupling constant and mass renormalizations are also calculated. [ABSTRACT FROM AUTHOR]

In the present paper, a particular form of Slavnov–Taylor identities for the Curci–Ferrari model is deduced. This model consist of Yang–Mills theory in a particular nonlinear covariant gauge, supplemented with mass terms for gluons and ghosts. It can be used as a regularization for the Yang–Mills theory preserving simple Slavnov–Taylor identities. Employing these identities, two nonrenormalization theorems are proved that reduce the number of independent renormalization factors from five to three. These new relations are verified by a comparison to the already known three-loops renormalization factors. These relations include, as a particular case, the corresponding known identities in Yang–Mills theory in Landau gauge. [ABSTRACT FROM AUTHOR]

The off-shell Batalin-Vilkovysky (BV) realization has been constructed for N = 1, d = 10 super-Yang-Mills theory with seven auxiliary fields. This becomes possible due to the materialized ghost phenomenon. Namely, supersymmetry ghosts are coordinates on a manifold B of ten-dimensional spinors with the pure spinors cut out. Auxiliary fields are sections of a bundle over B, and supersymmetry transformations are nonlinear in ghosts. By integrating out the auxiliary fields, we obtain an on-shell supersymmetric BV action with quadratic terms in the antifields. Exactly this on-shell BV action was obtained in our previous paper after integration out of auxiliary fields in the framework of a pure spinor superfield formalism. [ABSTRACT FROM AUTHOR]

In this paper, we revisit the isomorphism SU(2) ⊗ SU(2) ≅ SO(4) to apply to some subjects in Quantum Computation and Mathematical Physics. The unitary matrix Q by Makhlin giving the isomorphism as an adjoint action is studied and generalized from a different point of view. Some problems are also presented. In particular, the homogeneous manifold SU(2n)/SO(2n) which characterizes entanglements in the case of n = 2 is studied, and a clear-cut calculation of the universal Yang–Mills action in (hep-th/0602204) is given for the abelian case. [ABSTRACT FROM AUTHOR]

The aim of this paper is to compare the renormalizations of the infinite parts of the effective action and quantum equation of motion in gauge fields theory with structural group SU (N) in the one-loop approach and to show that they do not coincide. To this end, we use the background formalism, in which a gauge field is decomposed into the sum of a classical (background) field and a quantum field: A = B + gQ. The appearance of an additional factor, which provides the recovery of the equality of renormalizations of equations and action, is explained by comparison with results of the standard renormalization theory of Yang-Mills fields. Bibliography: 7 titles. [ABSTRACT FROM AUTHOR]

This paper proposes an algorithm for the Lie symmetries investigation in the case of a 2D Hamiltonian system. General Lie operators are deduced firstly and, in the the next step, the associated Lie invariants are derived. The 2D Yang-Mills mechanical model is chosen as a test model for this method. [ABSTRACT FROM AUTHOR]

We determine the nilpotent BRST and anti-BRST transformations for the Cho-Faddeev-Niemi variables for the $SU\!(2)$ Yang-Mills theory based on the new interpretation given in a previous paper of the Cho-Faddeev-Niemi decomposition. This gives a firm ground for performing the BRST quantization of the Yang-Mills theory written in terms of the Cho-Faddeev-Niemi variables. We propose also a modified version of the new maximal Abelian gauge which could play an important role in the reduction to the original Yang-Mills theory. [ABSTRACT FROM AUTHOR]

In this paper it is shown that the gauge fixing term is not only gauge fixing term in D dimensions, but also the mass term for gauge field in (D+2)-dimensional superspace [or (D-2)-dimensional space], more importantly the kinetic term for the gauge modes g(x) is the so-called (D-2)-dimensional SU(N)×SU(N) principal chiral model. The results conform Migdal's scheme about the connection between four-dimensional gauge field and two-dimensional chiral system. And the recursion relation can be generalized to D dimensions gauge theories with chiral models in D-2 dimensions. With the new local order parameter for Yang–Mills field |[sub D-2], the results are consistent with lattice results qualitatively: there is no phase transition in low dimensions (D≤4), while in higher dimensions first-order phase transition appears between strong coupling region and weak coupling region. [ABSTRACT FROM AUTHOR]

In the present paper, the Faddeev-Popov determinant arising in the partially-dual decomposition of the SU(2) Yang-Mills field is studied. Bibliography: 4 titles. [ABSTRACT FROM AUTHOR]

In this paper we give a unified proof to the soliton resolution conjecture along a sequence of times, for the semilinear focusing energy critical wave equations in the radial case and two dimensional equivariant wave map equations, including the four dimensional radial Yang Mills equation, without using outer energy type inequalities. Such inequalities have played a crucial role in previous works with similar results. Roughly speaking, we prove that along a sequence of times tn→T+ (the maximal time of existence), the solution decouples to a sum of rescaled solitons and a term vanishing in the energy space, plus a free radiation term in the global case or a regular part in the finite time blow up case. The main difficulty is that in general (for instance for the radial four dimensional Yang Mills case and the radial six dimensional semilinear wave case) we do not have a favorable outer energy inequality for the associated linear wave equations. Our main new input is the simultaneous use of two virial identities. [ABSTRACT FROM AUTHOR]

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Using the double-copy construction of Yang-Mills-Einstein theories formulated in our earlier work, we obtain compact presentations for single-trace Yang-Mills-Einstein tree amplitudes with up to five external gravitons and an arbitrary number of gluons. These are written as linear combinations of color-ordered Yang-Mills trees, where the coefficients are given by color/kinematics-satisfying numerators in a Yang-Mills + ϕ theory. The construction outlined in this paper holds in general dimension and extends straightforwardly to supergravity theories. For one, two, and three external gravitons, our expressions give identical or simpler presentations of amplitudes already constructed through string-theory considerations or the scattering equations formalism. Our results are based on color/kinematics duality and gauge invariance, and strongly hint at a recursive structure underlying the single-trace amplitudes with an arbitrary number of gravitons. We also present explicit expressions for all-loop single-graviton Einstein-Yang-Mills amplitudes in terms of Yang-Mills amplitudes and, through gauge invariance, derive new all-loop amplitude relations for Yang-Mills theory. [ABSTRACT FROM AUTHOR]

In this paper, we shall analyze a three dimensional supersymmetry theory with $$\mathcal {N} = 2$$ supersymmetry. We will analyze the quantization of this theory, in the presence of a boundary. The effective Lagrangian used in the path integral quantization of this theory, will be given by the sum of the gauge fixing term and the ghost term with the original classical Lagrangian. Even though the supersymmetry of this effective Lagrangian will also be broken due to the presence of a boundary, it will be demonstrated that half of the supersymmetry of this theory can be preserved by adding a boundary Lagrangian to the effective bulk Lagrangian. The supersymmetric transformation of this new boundary Lagrangian will exactly cancel the boundary term generated from the supersymmetric transformation of the effective bulk Lagrangian. We will analyze the Slavnov-Taylor identity for this $$\mathcal {N} = 2$$ Yang-Mills theory with a boundary. [ABSTRACT FROM AUTHOR]

We consider structure constants of single trace operators in planar $$ \mathcal{N}=4 $$ Super-Yang-Mills theory within the hexagon framework. The standard procedure for forming a three point function out of two hexagons develops divergences when the effects of virtual particles wrapping around the operators are taken into account. In this paper, we explain how to renormalize these divergences away and obtain definite predictions, at the leading wrapping order, for some of the structure constants that parameterize the OPE of two chiral primaries. We test our method at weak coupling against the four loop planar correction to the BPS-BPS-Konishi OPE coefficient, derived recently in the field theory. At strong coupling, we compare our expressions with the structure constants obtained in string theory for three semiclassical strings. [ABSTRACT FROM AUTHOR]

We give three short proofs of the Makeenko-Migdal equation for the Yang-Mills measure on the plane, two using the edge variables and one using the loop or lasso variables. Our proofs are significantly simpler than the earlier pioneering rigorous proofs given by Lévy and by Dahlqvist. In particular, our proofs are 'local' in nature, in that they involve only derivatives with respect to variables adjacent to the crossing in question. In an accompanying paper with Gabriel, we show that two of our proofs can be adapted to the case of Yang-Mills theory on any compact surface. [ABSTRACT FROM AUTHOR]

In this paper we construct new solutions of the Kähler-Yang-Mills equations, by applying dimensional reduction methods to the product of the complex projective line with a compact Riemann surface. The resulting equations, which we call gravitating vortex equations, describe abelian vortices on the Riemann surface with back reaction of the metric. As a particular case of these gravitating vortices on the Riemann sphere we find solutions of the Einstein-Bogomol'nyi equations, which physically correspond to Nielsen-Olesen cosmic strings in the Bogomol'nyi phase. We use this to provide a Geometric Invariant Theory interpretation of an existence result by Y. Yang for the Einstein-Bogomol'nyi equations, applying a criterion due to G. Székelyhidi. [ABSTRACT FROM AUTHOR]

The double copy relates scattering amplitudes in gauge and gravity theories. In this paper, we expand the scope of the double copy to construct spacetime metrics through a systematic perturbative expansion. The perturbative procedure is based on direct calculation in Yang-Mills theory, followed by squaring the numerator of certain perturbative diagrams as specified by the double-copy algorithm. The simplest spherically symmetric, stationary spacetime from the point of view of this procedure is a particular member of the Janis-Newman-Winicour family of naked singularities. Our work paves the way for applications of the double copy to physically interesting problems such as perturbative black-hole scattering. [ABSTRACT FROM AUTHOR]

We continue with the analysis of finite temperature corrections to the Tachyon mass in intersecting branes which was initiated in [1]. In this paper we extend the computation to the case of intersecting D3 branes by considering a setup of two intersecting branes in flat-space background. A holographic model dual to BCS superconductor consisting of intersecting D8 branes in D4 brane background was proposed in [2]. The background considered here is a simplified configuration of this dual model. We compute the one-loop Tachyon amplitude in the Yang-Mills approximation and show that the result is finite. Analyzing the amplitudes further we numerically compute the transition temperature at which the Tachyon becomes massless. The analytic expressions for the one-loop amplitudes obtained here reduce to those for intersecting D1 branes obtained in [1] as well as those for intersecting D2 branes. [ABSTRACT FROM AUTHOR]

In 2005, Briani and Rampazzo [4], using the results of [10, 12-14], gave a density approach to Hamilton-Jacobi equations with t-measurable Hamiltonians. In this paper we firstly give more details and do more investigation on viscosity solutions for Hamilton-Jacobi equations. Then we show, using an important result of [4], the existence and uniqueness of viscosity solutions to the Vlasov relativistic equation in Yang- Mills charged Bianchi space times, with non zero mass. Thirdly, we clearly display, in the case of the Vlasov equation, the optimal control problem. To our knowledge, the method and techniques used here are original and thus, totally different from those used in [1, 5, 6, 8, 13, 15, 16] who have studied the same equation. [ABSTRACT FROM AUTHOR]

We study dynamics of multi-soliton solutions of anti-self-dual Yang-Mills equations for G = GL(2, ℂ) in four-dimensional spaces. The one-soliton solution can be interpreted as a codimension-one soliton in four-dimensional spaces because the principal peak of action density localizes on a three-dimensional hyperplane. We call it the soliton wall. We prove that in the asymptotic region, the n-soliton solution possesses n isolated localized lumps of action density, and interpret it as n intersecting soliton walls. More precisely, each action density lump is essentially the same as a soliton wall because it preserves its shape and "velocity" except for a position shift of principal peak in the scattering process. The position shift results from the nonlinear interactions of the multi-solitons and is called the phase shift. We calculate the phase shift factors explicitly and find that the action densities can be real-valued in three kind of signatures. Finally, we show that the gauge group can be G = SU(2) in the Ultrahyperbolic space 핌 (the split signature (+, +, −, −)). This implies that the intersecting soliton walls could be realized in all region in N=2 string theories. It is remarkable that quasideterminants dramatically simplify the calculations and proofs. [ABSTRACT FROM AUTHOR]

We consider known expressions for the eigenvalue of the Balitsky-Fadin-Kuraev-Lipatov (BFKL) equation in N = 4 super Yang-Mills theory as a real valued function of two variables. We define new real valued functions of two complex conjugate variables that have a definite complexity analogous to the weight of the nested harmonic sums. We argue that those functions span a general space of functions for the BFKL eigenvalue at any order of the perturbation theory. [ABSTRACT FROM AUTHOR]

We present a new expression for the partition function of the refined Chern-Simons theory on S3 with an arbitrary gauge group, which is explicitly equal to 1 when the coupling constant is zero. Using this form of the partition function we show that the previously known Krefl-Schwarz representation of the partition function of the refined Chern-Simons theory on S3 can be generalized to all simply laced algebras. For all non-simply laced gauge algebras, we derive similar representations of that partition function, which makes it possible to transform it into a product of multiple sine functions aiming at the further establishment of duality with the refined topological strings. [ABSTRACT FROM AUTHOR]

The analytic property of the Sasa-Satsuma equation has been well-explored via using an array of mathematical tools (such as the inverse scattering transformation, the Hirota bilinear method and the Darboux transformation). This paper devotes to exploring geometric properties of this equation via the zero curvature representation in terms of the language in Yang-Mills theory. The generalized Landau-Lifshitz type model of Sym-Pohlmeyer moving curves evolving in the symmetric Lie algebra g = k ⊕ m with initial data being suitably restricted is gauge equivalent to the Sasa-Satsuma equation. This gives a geometric realization of the Sasa-Satsuma equation. [ABSTRACT FROM AUTHOR]

In this paper, we analyze the quantization of Yang–Mills theory in the de Sitter spacetime. It is observed that the Faddeev–Popov ghost propagator is divergent in this spacetime. However, this divergence is removed by using an effective propagator, which is suitable for perturbation theory. To show that the quantization of Yang–Mills theory in the de Sitter is consistent, we quantize it using first-class constraints in the temporal gauge. We also demonstrate that this is equivalent to quantizing the theory in the Lorentz gauge. [ABSTRACT FROM AUTHOR]

We study the Wilson line defect half-indices of 3d N = 2 supersymmetric SU(N) Chern-Simons theories of level k ≤ – N with Neumann boundary conditions for the gauge fields, together with 2d Fermi multiplets and fundamental 3d chiral multiplets to cancel the gauge anomaly. We derive some exact results and also make some conjectures based on expansions of the q-series. We find several interesting connections with special functions known in the literature, including Rogers-Ramanujan functions for which we conjecture integral representations, and the appearance of Appell-Lerch sums for certain Wilson line half-index grand canonical ensembles which reveal an unexpected appearance of mock modular functions. We also find intriguing q-difference equations relating half-indices to Wilson line half-indices. Some of these results also have a description in terms of a dual theory with Dirichlet boundary conditions for the vector multiplet in the dual theory. [ABSTRACT FROM AUTHOR]