# 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} }

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

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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…

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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.…

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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

- MathematicsJournal 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…

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- 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…

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- 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…

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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
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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…

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