Bethe-State Counting and the Witten Index

TL;DR

This paper connects the counting of Bethe states in quantum integrable models with twisted boundary conditions to the Witten index of 2d supersymmetric gauge theories, providing new formulas for specific models.

Contribution

It introduces a novel approach to counting Bethe states using supersymmetric gauge theory indices and proposes explicit formulas for complex models like SU(3) spin chain.

Findings

Bethe states counted via Witten index for models with twisted boundaries

New restricted occupancy problem for nested Bethe ansatz models

Explicit formulas for Bethe state counts in SU(3) and t-J models

Abstract

We count the Bethe states of quantum integrable models with twisted boundary conditions using the Witten index of 2d supersymmetric gauge theories. For multi-component models solvable by the nested Bethe ansatz, the result is a novel restricted occupancy problem. For the SU(3) spin chain and the t-J model, we propose formulae for the solution count on singular loci in the space of twist parameters.