Bethe/Gauge correspondence on curved spaces

TL;DR

This paper explores the Bethe/gauge correspondence on curved spaces, linking supersymmetric vacua to quantum integrable systems, and computes key operators related to topological field theories and Bethe state norms.

Contribution

It extends the Bethe/gauge correspondence to curved spaces and computes the handle gluing operator H for twisted supersymmetric theories.

Findings

Computed the handle gluing operator H for topologically twisted theories.

Discussed the Gaudin conjecture and its relation to the operator H.

Connected supersymmetric vacua with stationary states of quantum integrable systems.

Abstract

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 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.