The star-triangle relation and 3d superconformal indices

TL;DR

This paper explores the connection between 3d superconformal indices and the Yang-Baxter equation, providing explicit solutions and analyzing their implications for lattice models and flavor symmetry breaking.

Contribution

It expresses 3d superconformal indices in terms of q-special functions related to the Yang-Baxter equation and computes the free energy for a specific lattice system.

Findings

Explicit solutions to star-triangle relations using q-special functions

Free energy per spin for a 2D monopole-spin lattice system

Superconformal indices reduce to delta functions under symmetry breaking

Abstract

Superconformal indices of 3d N=2 supersymmetric field theories are investigated from the Yang-Baxter equation point of view. Solutions of the star-triangle relation, vertex and IRF Yang-Baxter equations are expressed in terms of the q-special functions associated with these 3d indices. For a two-dimensional monopole-spin system on the square lattice a free energy per spin is explicitly determined. Similar to the partition functions, superconformal indices of 3d theories with the chiral symmetry breaking reduce to Dirac delta functions with the support on chemical potentials of the preserved flavor groups.