# Bethe/gauge correspondence on curved spaces

@article{Nekrasov2014BethegaugeCO,
title={Bethe/gauge correspondence on curved spaces},
author={Nikita A. Nekrasov and Samson L. Shatashvili},
journal={Journal of High Energy Physics},
year={2014},
volume={2015},
pages={1-17}
}
• Published 23 May 2014
• Physics
• Journal of High Energy Physics
A bstractBethe/gauge correspondence identifies supersymmetric vacua of massive gauge theories invariant under the two dimensional N$$\mathcal{N}$$ = 2 Poincare supersymmetry with the stationary states of some quantum integrable system. The supersymmetric theory can be twisted in a number of ways, producing a topological field theory. For these theories we compute the handle gluing operator ℋ. We also discuss the Gaudin conjecture on the norm of Bethe states and its connection to ℋ.
85 Citations
Solution of quantum integrable systems from quiver gauge theories
• Physics, Mathematics
• 2015
A bstractWe construct new integrable systems describing particles with internal spin from four-dimensional N$$\mathcal{N}$$ = 2 quiver gauge theories. The models can be quantized and solved exactly
Twisted indices of 3 d N = 4 gauge theories and enumerative geometry of quasi-maps
• Mathematics
• 2019
We explore the geometric interpretation of the twisted index of 3d N = 4 gauge theories on S1 × Σ where Σ is a closed Riemann surface. We focus on a rich class of supersymmetric quiver gauge theories
Expanding the Bethe/Gauge dictionary
• Physics
• 2017
A bstractWe expand the Bethe/Gauge dictionary between the XXX Heisenberg spin chain and 2d N$$\mathcal{N}$$ = (2, 2) supersymmetric gauge theories to include aspects of the algebraic Bethe ansatz.
Two-dimensional supersymmetric gauge theories with exceptional gauge groups
• Physics
• 2018
We apply the recent proposal for mirrors of nonabelian (2,2) supersymmetric two-dimensional gauge theories to make predictions for two-dimensional supersymmetric gauge theories with exceptional gauge
Topologically twisted SUSY gauge theory, gauge-Bethe correspondence and quantum cohomology
• Mathematics
Journal of High Energy Physics
• 2019
A bstractWe calculate the partition function and correlation functions in A-twisted 2d N$$\mathcal{N}$$ = (2, 2) U(N) gauge theories and topologically twisted 3d N$$\mathcal{N}$$ = 2 U(N) gauge
The equivariant A-twist and gauged linear sigma models on the two-sphere
• Mathematics
• 2015
A bstractWe study two-dimensional N=2,2$$\mathcal{N}=\left(2,\;2\right)$$ supersymmetric gauged linear sigma models (GLSM) on the Ω-deformed sphere, SΩ2, which is a one-parameter deformation of the
Comments on twisted indices in 3d supersymmetric gauge theories
• Mathematics
• 2016
A bstractWe study three-dimensional N$$\mathcal{N}$$ = 2 supersymmetric gauge theories on Σg × S1 with a topological twist along Σg , a genus-g Riemann surface. The twisted supersymmetric index at
Web of Seiberg-like dualities for 3d $\mathcal{N}=2$ quivers
• Mathematics
• 2021
We construct Seiberg-like dualities of 3d N = 2 general quiver gauge theories with unitary, symplectic and orthogonal gauge groups coupled to fundamental and bifundamental matter ﬁelds. We illustrate
Equivariant Verlinde Formula from Fivebranes and Vortices
• Mathematics
• 2015
We study complex Chern–Simons theory on a Seifert manifold M3 by embedding it into string theory. We show that complex Chern–Simons theory on M3 is equivalent to a topologically twisted
Dynamics of Two-Dimensional $\mathcal{N}=(2,2)$ Supersymmetric Theories with Semichiral Superfields I
• Physics
• 2014
We analyze the dynamics of a general two-dimensional $\mathcal{N}=(2,2)$ gauged linear sigma model with semichiral superfields. By computing the elliptic genera, we study the vacuum structure of the

## References

SHOWING 1-10 OF 41 REFERENCES
Higgs Bundles, Gauge Theories and Quantum Groups
• Mathematics, Physics
• 2007
The appearance of the Bethe Ansatz equation for the Nonlinear Schrödinger equation in the equivariant integration over the moduli space of Higgs bundles is revisited. We argue that the wave functions
Two-dimensional Gauge Theories and Quantum Integrable Systems
• Physics
• 2007
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
Quantization of Integrable Systems and Four Dimensional Gauge Theories
• Physics, Mathematics
• 2010
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
Quantum Integrability and Supersymmetric Vacua
• Physics, Mathematics
• 2009
Supersymmetric vacua of two dimensional N = 4 gauge theories with matter, softly broken by the twisted masses down to N = 2, are shown to be in one-to-one correspon- dence with the eigenstates of