scholarly journals Five-Dimensional Gauge Theories and Whitham–Toda Equation

1997 ◽  
Vol 12 (29) ◽  
pp. 2183-2191 ◽  
Author(s):  
Masato Hisakado
Keyword(s):  
Gauge Theory ◽  
Toda Lattice ◽  
Gauge Theories ◽  
Toda Chain ◽  
Charge Conjugation ◽  
Two Dimensional ◽  
Toda Equation ◽  
Toda Lattice Hierarchy

The five-dimensional supersymmetric SU (N) gauge theory is studied in the framework of the relativistic Toda chain. This equation can be embedded in two-dimensional Toda lattice hierarchy. This system has the conjugate structure which corresponds to the charge conjugation.

scholarly journals Faces of Relativistic Toda Chain

1997 ◽  
Vol 12 (15) ◽  
pp. 2675-2724 ◽  
Author(s):  
S. Kharchev ◽  
A. Mironov ◽  
A. Zhedanov
Keyword(s):  
Orthogonal Polynomial ◽  
Toda Lattice ◽  
Toda Chain ◽  
Polynomial Systems ◽  
Function Approach ◽  
Unitary Matrix ◽  
Lax Representation ◽  
Two Dimensional ◽  
Two Component ◽  
Toda Lattice Hierarchy

We demonstrate that the generalization of the relativistic Toda chain (RTC) is a special reduction of two-dimensional Toda lattice hierarchy (2DTL). This reduction implies that the RTC is gauge equivalent to the discrete AKNS hierarchy and, which is the same, to the two-component Volterra hierarchy while its forced (semi-infinite) variant is described by the unitary matrix integral. The integrable properties of the RTC hierarchy are revealed in different frameworks of the Lax representation, orthogonal polynomial systems, and τ-function approach. Relativistic Toda molecule hierarchy is also considered, along with the forced RTC. Some applications to biorthogonal polynomial systems are discussed.

WEYL FERMION FUNCTIONAL INTEGRAL AND TWO-DIMENSIONAL GAUGE THEORIES

1990 ◽  
Vol 05 (14) ◽  
pp. 2839-2851
Author(s):  
J.L. ALONSO ◽  
J.L. CORTÉS ◽  
E. RIVAS
Keyword(s):  
Gauge Theory ◽  
Gauge Theories ◽  
Functional Integral ◽  
Integral Approach ◽  
Two Dimensional ◽  
Regularization Scheme ◽  
Schwinger Model ◽  
Left Handed ◽  
Definition Of ◽  
Weyl Fermion

In the path integral approach we introduce a general regularization scheme for a Weyl fermionic measure. This allows us to study the functional integral formulation of a two-dimensional U(1) gauge theory with an arbitrary content of left-handed and right-handed fermions. A particular result is that, in contrast with a regularization of the fermionic measure based on a unique Dirac operator, by taking the Dirac fermionic measure as a product of two independent Weyl fermionic measures a consistent and unitary result can be obtained for the Chiral Schwinger Model (CSM) as a byproduct of the arbitrariness in the definition of the fermionic measure.

scholarly journals Quantum spin systems and supersymmetric gauge theories. Part I

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Norton Lee ◽  
Nikita Nekrasov
Keyword(s):  
Gauge Theory ◽  
Spin Chain ◽  
Gauge Theories ◽  
Surface Defects ◽  
Toda Chain ◽  
Quantum Spin ◽  
Spin Systems ◽  
Quantum Spin Systems ◽  
Supersymmetric Gauge Theories ◽  
Supersymmetric Gauge

Abstract The relation between supersymmetric gauge theories in four dimensions and quantum spin systems is exploited to find an explicit formula for the Jost function of the N site $$ \mathfrak{sl} $$ sl 2X X X spin chain (for infinite dimensional complex spin representations), as well as the SLN Gaudin system, which reduces, in a limiting case, to that of the N-particle periodic Toda chain. Using the non-perturbative Dyson-Schwinger equations of the supersymmetric gauge theory we establish relations between the spin chain commuting Hamiltonians with the twisted chiral ring of gauge theory. Along the way we explore the chamber dependence of the supersymmetric partition function, also the expectation value of the surface defects, giving new evidence for the AGT conjecture.

scholarly journals Notes on two-dimensional pure supersymmetric gauge theories

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Wei Gu ◽  
Eric Sharpe ◽  
Hao Zou
Keyword(s):  
Gauge Theory ◽  
Degrees Of Freedom ◽  
Gauge Theories ◽  
Universal Covering ◽  
Chiral Multiplet ◽  
Two Dimensional ◽  
Supersymmetric Gauge Theories ◽  
Gauge Groups ◽  
Pure Gauge ◽  
Supersymmetric Gauge

Abstract In this note we study IR limits of pure two-dimensional supersymmetric gauge theories with semisimple non-simply-connected gauge groups including SU(k)/ℤk, SO(2k)/ℤ2, Sp(2k)/ℤ2, E6/ℤ3, and E7/ℤ2 for various discrete theta angles, both directly in the gauge theory and also in nonabelian mirrors, extending a classification begun in previous work. We find in each case that there are supersymmetric vacua for precisely one value of the discrete theta angle, and no supersymmetric vacua for other values, hence supersymmetry is broken in the IR for most discrete theta angles. Furthermore, for the one distinguished value of the discrete theta angle for which supersymmetry is unbroken, the theory has as many twisted chiral multiplet degrees of freedom in the IR as the rank. We take this opportunity to further develop the technology of nonabelian mirrors to discuss how the mirror to a G gauge theory differs from the mirror to a G/K gauge theory for K a subgroup of the center of G. In particular, the discrete theta angles in these cases are considerably more intricate than those of the pure gauge theories studied in previous papers, so we discuss the realization of these more complex discrete theta angles in the mirror construction. We find that discrete theta angles, both in the original gauge theory and their mirrors, are intimately related to the description of centers of universal covering groups as quotients of weight lattices by root sublattices. We perform numerous consistency checks, comparing results against basic group-theoretic relations as well as with decomposition, which describes how two-dimensional theories with one-form symmetries (such as pure gauge theories with nontrivial centers) decompose into disjoint unions, in this case of pure gauge theories with quotiented gauge groups and discrete theta angles.

scholarly journals NOTE ON TWO-DIMENSIONAL NONLINEAR GAUGE THEORIES

2000 ◽  
Vol 15 (33) ◽  
pp. 2047-2055 ◽  
Author(s):  
C. BIZDADEA
Keyword(s):  
Gauge Theory ◽  
Gauge Theories ◽  
Higher Dimensions ◽  
Two Dimensional ◽  
Nonlinear Gauge

A two-dimensional nonlinear gauge theory that can be proposed for generalization to higher dimensions is derived by means of cohomological arguments.

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