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.
Highlights
Seiberg dual theories [43, 44]
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
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
Summary
Where T is the unit circle of positive orientation. This is a q-beta sum-integral associated with 3d superconformal indices. The proof of the theorem is presented in [27]. Let us define the following generalized q-gamma function as a combination of four q-gamma functions and zm and am: Γq(a, n; z, m). One has the following inversion relation: Γq(a, n; z, m)Γq(b, −n; z, m) = 1, ab = q. For other possible values of the integers n and m one gets the same result due to the properties of q-Pochhammer symbols. We can rewrite the above q-beta sum-integral in the following compact form.
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