Bethe-State Counting and the Witten Index
High Energy Physics - Theory
2023-10-12 v1 Statistical Mechanics
Mathematical Physics
math.MP
Exactly Solvable and Integrable Systems
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.
Cite
@article{arxiv.2210.07116,
title = {Bethe-State Counting and the Witten Index},
author = {Hongfei Shu and Peng Zhao and Rui-Dong Zhu and Hao Zou},
journal= {arXiv preprint arXiv:2210.07116},
year = {2023}
}
Comments
7 pages (including the appendix and reference), 5 figures and 1 table