The star-triangle relation and 3d superconformal indices

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.

20 pages, v2: minor corrections, comments and refs. added

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• Integrable lattice spin models from supersymmetric dualities
• Mathematical structures behind supersymmetric dualities
• Lens elliptic gamma function solution of the Yang-Baxter equation at roots of unity
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• A New Integrable Ising-type Model from 2d $\mathcal{N}$=(2,2) Dualities
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• On Bailey pairs for $\mathcal{N}=2$ supersymmetric gauge theories on $S_b^3/{\mathbb{Z}}_r$
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