Bethe-State Counting and the Witten Index

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.

7 pages (including the appendix and reference), 5 figures and 1 table

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Cited by in corpus (4)

• Spin-$s$ Rational $Q$-system
• Counting Bethe States in Twisted Spin Chains
• Bethe/Gauge Correspondence for $A_N$ Spin Chains with Integrable Boundaries
• Spin-$s$ $Q$-systems: Twist and Open Boundaries