Related papers: Quantum Integrable Systems from Supergroup Gauge T…
This note gives a brief review of the integrable structures presented in the Seiberg-Witten approach to the N=2 SUSY gauge theories with emphasize on the case of the gauge theories with matter hypermultiplets included (described by spin…
This PhD thesis explores the similarities between integrable spin chains and quantum field theories, such as Super Yang Mills. We first study integrable spin chains and build explicitly a polynomial "Backlund flow" and polynomial…
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…
We discuss supersymmetric Yang-Mills theories with the multiple scales in the brane language. The issue concerns N=2 SUSY gauge theories with massive fundamental matter including the UV finite case of $n_{f}=2n_c$, theories involving…
All supersymmetric gauge theories based on simple groups which have an affine quantum moduli space, i.e. one generated by gauge invariants with no relations, W=0, and anomaly matching at the origin, are classified. It is shown that the only…
We construct integrable modifications of 2d lattice gauge theories with finite gauge groups.
We present an algebraic study of a kind of quantum systems belonging to a family of superintegrable Hamiltonian systems in terms of shape-invariant intertwinig operators, that span pairs of Lie algebras like $(su(n),so(2n))$ or…
We discuss various dualities, relating integrable systems and show that these dualities are explained in the framework of Hamiltonian and Poisson reductions. The dualities we study shed some light on the known integrable systems as well as…
Superintegrable systems are classical and quantum Hamiltonian systems which enjoy much symmetry and structure that permit their solubility via analytic and even, algebraic means. They include such well-known and important models as the…
We summarize recent results on the resolution of two intimately related problems, one physical, the other mathematical. The first deals with the resolution of the non-perturbative low energy dynamics of certain N=2 supersymmetric Yang-Mills…
In this note, we use techniques from integrable systems to study relations between gauge theories. The Gauge/Bethe correspondence, introduced by Nekrasov and Shatashvili, identifies the supersymmetric ground states of an N=(2,2)…
We consider some examples of quantum super-integrable systems and the associated nonlinear extensions of Lie algebras. The intimate relationship between super-integrability and exact solvability is illustrated. Eigenfunctions are…
This note is an extension of [DZ23] there the supersymmetric vacua of three-dimensional $\mathcal{N}=2$ gauge theories with matter are shown to be in one-to-one correspondence with the eigenstate of $\text{XXZ}$ integrable spin chain…
We continue to investigate the relationship between the infrared physics of N=2 supersymmetric gauge theories in four dimensions and various integrable models such as Gaudin, Calogero-Moser and quantum spin chains. We prove interesting…
We formulate $Q$-systems for the closed XXZ, open XXX and open quantum-group-invariant XXZ quantum spin chains. Polynomial solutions of these $Q$-systems can be found efficiently, which in turn lead directly to the admissible solutions of…
The relation between solutions to Helmholtz's equation on the sphere $S^{n-1}$ and the $[{\gr sl}(2)]^n$ Gaudin spin chain is clarified. The joint eigenfuctions of the Laplacian and a complete set of commuting second order operators…
Abelian and non-Abelian gauge theories are of central importance in many areas of physics. In condensed matter physics, Abelian U(1) lattice gauge theories arise in the description of certain quantum spin liquids. In quantum information…
A quantum integrable spin chain model associated with the $G_2$ exceptional Lie algebra is studied. By using the fusion technique, the closed recursive relations among the fused transfer matrices are obtained. These identities allow us to…
We construct lattice actions for a variety of (2,2) supersymmetric gauge theories in two dimensions with matter fields interacting via a superpotential.
In this work, we present a brief but insightful overview of the gauge theories, which are defined on $ n $-dimensional lattices by using finite gauge groups, in order to show how they can be interpreted as a Hamiltonian system with…