Related papers: Relating Gauge Theories via Gauge/Bethe Correspond…
The Gauge/Bethe correspondence of Nekrasov and Shatashvili relates the spectrum of integrable spin chains to the ground states of supersymmetric gauge theories. Up to now, this correspondence has been an observation; the underlying reason…
In this article, we provide a short review (written in Chinese) on the Bethe/Gauge correspondence. We first explain the basic idea in an explicit example of the correspondence between XXX spin chains and 2d $\mathcal{N}=(2,2)$ gauge…
Bethe/gauge correspondence identifies supersymmetric vacua of massive gauge theories invariant under the two dimensional N=2 Poincare supersymmetry with the stationary states of some quantum integrable system. The supersymmetric theory can…
We continue the survey initiated in arXiv:2012.14197 to explore the Bethe/Gauge correspondence between supersymmetric SO/Sp gauge theories in 2d/3d/4d and open spin chain with integrable boundaries. We collect the known Bethe ansatz…
We construct new integrable systems describing particles with internal spin from four-dimensional $\mathcal{N}=2$ quiver gauge theories. The models can be quantized and solved exactly using the quantum inverse scattering method and also…
We study the Gauge/Bethe correspondence for two-dimensional $\mathcal{N}=(2,2)$ supersymmetric quiver gauge theories associated with toric Calabi-Yau three-folds, whose BPS algebras have recently been identified as the quiver Yangians. We…
In this paper the relation between 2d topological gauge theories and Bethe Ansatz equations is reviewed. In addition we present some new results and clarifications. We hope the relations discussed here are particular examples of more…
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…
In this article, we extend the work of arXiv:0901.4744 to a Bethe/Gauge correspondence between 2d (or resp. 3d) SO/Sp gauge theories and open XXX (resp. XXZ) spin chains with diagonal boundary conditions. The case of linear quiver gauge…
The Gauge/YBE correspondence states a surprising connection between solutions to the Yang-Baxter equation with spectral parameters and partition functions of supersymmetric quiver gauge theories. This correspondence has lead to systematic…
We present a string theory realization for the correspondence between quantum integrable models and supersymmetric gauge theories. The quantization results from summing the effects of fundamental strings winding around a compact direction.…
We discuss the possible extensions of Bethe/gauge correspondence to quantum integrable systems based on the super-Lie algebras of A type. Along the way we propose the analogues of Nakajima quiver varieties whose cohomology and K-theory…
In [1, 2], Nekrasov applied the Bethe/gauge correspondence to derive the $\mathfrak{su}\, (2)$ XXX spin-chain coordinate Bethe wavefunction from the IR limit of a 2D $\mathcal{N}=(2, 2)$ supersymmetric $A_1$ quiver gauge theory with an…
We investigate the correspondence between two dimensional topological gauge theories and quantum integrable systems discovered by Moore, Nekrasov, Shatashvili. This correspondence means that the hidden quantum integrable structure exists in…
We discuss Gubser-Klebanov-Polyakov proposal for the gauge/string theory correspondence for gauge theories in curved space. Specifically, we consider Klebanov-Tseytlin cascading gauge theory compactified on S^3. We explain regime when this…
Integrable models of statistical mechanics play a prominent role in modern mathematical physics, especially in conformal field theory, knot theory, combinatorics, topology, etc. In this brief review, we discuss a program of constructing…
In this paper, we give a new effective superpotential that makes clear Bethe/Gauge correspondence between 2d (and 3d) $\text{SO/Sp}$ gauge theories and open $\text{XXX}$ (and $\text{XXZ}$) spin chains with diagonal boundary conditions, and…
Bethe/Gauge correspondence as it is usually stated is ill-defined in five dimensions and needs a "non-perturbative" completion; a related problem also appears in three dimensions. It has been suggested that this problem, probably due to…
To analyse pure ${\cal N}=2$ $SU(2)$ gauge theory in the Nekrasov-Shatashvili (NS) limit (or deformed Seiberg-Witten (SW)), we use the Ordinary Differential Equation/Integrable Model (ODE/IM) correspondence, and in particular its (broken)…
This report presents some studies of the gauge/string theory correspondence, a deep relation that is possible to establish between quantum field theories with local gauge symmetry and superstring theories including gravity. In its original…