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Bethe/Gauge Correspondence for SO/Sp Gauge Theories and Open Spin Chains

Taro Kimura, Rui-Dong Zhu

Abstract

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 theories is also considered.

Bethe/Gauge Correspondence for SO/Sp Gauge Theories and Open Spin Chains

Abstract

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 theories is also considered.

Paper Structure

This paper contains 22 sections, 160 equations.

Table of Contents

  1. Introduction
  2. The R-matrix and Integrable Spin Chains
  3. Reduction to XXZ chain
  4. Open spin chain
  5. Remark:
  6. Effective Twisted Superpotential of 3d $\mathcal{N}=2$ Theory and 2d $\mathcal{N}=(2,2)$ Theory
  7. 3d $\mathcal{N}=2$ theory
  8. Remark:
  9. 2d $\mathcal{N}=(2,2)$ theory
  10. Effective potential in 3d and 2d
  11. Dictionary between A-type Gauge Theories and Closed Spin Chains
  12. Vacuum Equations and Bathe Ansatz Equations of Open Spin Chain
  13. SO($2N$) theory
  14. SO($2N+1$) theory
  15. Sp($N$) theory
  16. ...and 7 more sections