scholarly journals Solution of quantum integrable systems from quiver gauge theories

2017 ◽  
Vol 2017 (2) ◽  
Author(s):  
Nick Dorey ◽  
Peng Zhao
Keyword(s):  
Integrable Systems ◽  
Gauge Theories ◽  
Quantum Integrable Systems

scholarly journals Quantum integrable systems from supergroup gauge theories

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Heng-Yu Chen ◽  
Taro Kimura ◽  
Norton Lee
Keyword(s):  
Partition Function ◽  
Integrable Systems ◽  
Spin Chain ◽  
Toda Lattice ◽  
Gauge Theories ◽  
Partition Functions ◽  
Characteristic Polynomials ◽  
Quantum Integrable Systems ◽  
Gauge Groups ◽  
Moser System

Abstract In this note, we establish several interesting connections between the super- group gauge theories and the super integrable systems, i.e. gauge theories with supergroups as their gauge groups and integrable systems defined on superalgebras. In particular, we construct the super-characteristic polynomials of super-Toda lattice and elliptic double Calogero-Moser system by considering certain orbifolded instanton partition functions of their corresponding supergroup gauge theories. We also derive an exotic generalization of 𝔰𝔩(2) XXX spin chain arising from the instanton partition function of SQCD with super- gauge group, and study its Bethe ansatz equation.

Quantum integrable systems of particles as gauge theories

1994 ◽  
Vol 100 (1) ◽  
pp. 874-878 ◽  
Author(s):  
A. Gorsky ◽  
N. Nekrasov
Keyword(s):  
Integrable Systems ◽  
Gauge Theories ◽  
Quantum Integrable Systems

scholarly journals Separation of variables in AdS/CFT: functional approach for the fishnet CFT

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Andrea Cavaglià ◽  
Nikolay Gromov ◽  
Fedor Levkovich-Maslyuk
Keyword(s):  
Integrable Systems ◽  
Density Operator ◽  
Numerical Evaluation ◽  
Lagrangian Density ◽  
Separation Of Variables ◽  
Functional Approach ◽  
Quantum Integrable Systems ◽  
Arbitrary State ◽  
Nontrivial Coupling ◽  
The One

Abstract The major simplification in a number of quantum integrable systems is the existence of special coordinates in which the eigenstates take a factorised form. Despite many years of studies, the basis realising the separation of variables (SoV) remains unknown in $$ \mathcal{N} $$ N = 4 SYM and similar models, even though it is widely believed they are integrable. In this paper we initiate the SoV approach for observables with nontrivial coupling dependence in a close cousin of $$ \mathcal{N} $$ N = 4 SYM — the fishnet 4D CFT. We develop the functional SoV formalism in this theory, which allows us to compute non-perturbatively some nontrivial observables in a form suitable for numerical evaluation. We present some applications of these methods. In particular, we discuss the possible SoV structure of the one-point correlators in presence of a defect, and write down a SoV-type expression for diagonal OPE coefficients involving an arbitrary state and the Lagrangian density operator. We believe that many of the findings of this paper can be applied in the $$ \mathcal{N} $$ N = 4 SYM case, as we speculate in the last part of the article.

Lecture on SUSY Gauge Theories and Integrable Systems

1997 ◽  
Vol 11 (26n27) ◽  
pp. 3093-3124
Author(s):  
A. Marshakov
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Integrable Systems ◽  
Gauge Theories ◽  
Toda Chain ◽  
Quantum Field ◽  
Standard Quantum ◽  
Integrable Equations ◽  
Complex Curves ◽  
Periodic Toda Chain

I consider main features of the formulation of the finite-gap solutions to integrable equations in terms of complex curves and generating 1-differential. The example of periodic Toda chain solutions is considered in detail. Recently found exact nonperturbative solutions to [Formula: see text] SUSY gauge theories are formulated using the methods of the theory of integrable systems and where possible the parallels between standard quantum field theory results and solutions to the integrable systems are discussed.

scholarly journals ALGEBRAIC ASPECT AND CONSTRUCTION OF LAX OPERATORS IN QUANTUM INTEGRABLE SYSTEMS

1995 ◽  
Vol 10 (40) ◽  
pp. 3113-3117 ◽  
Author(s):  
B. BASU-MALLICK ◽  
ANJAN KUNDU
Keyword(s):  
Integrable Systems ◽  
Integrable Models ◽  
Quantum Integrable Systems ◽  
Algebraic Construction ◽  
Algebraic Aspect ◽  
Quantum Integrable Models

An algebraic construction which is more general and closely connected with that of Faddeev,1 along with its application for generating different classes of quantum integrable models is summarized to complement the recent results of Ref. 1.

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