Boundary lines and Askey-Wilson type moments

TL;DR

This paper derives exact formulas for Wilson line defect half-indices in 3d N=2 gauge theories with boundary phases, expressing them as Askey-Wilson type moments, linking gauge theory and special functions.

Contribution

It introduces a novel formulation of line defect half-indices using Askey-Wilson moments, connecting gauge theory defects with special function integrals.

Findings

Exact closed-form expressions for line defect half-indices

Representation of indices as Askey-Wilson type moments

Dual description involving vortex line defects and singular monopole operators

Abstract

The Wilson line defect half-indices for 3d $\mathcal{N}=2$ gauge theories with boundary confining phases admit a formulation in terms of the Askey-Wilson type moments. In the dual Landau-Ginzburg description the dual line operators can be realized as vortex line defects which induce singular behavior of chiral multiplets associated with the minimal monopole operators, together with additional one-dimensional degrees of freedom. By incorporating such a singular structure as an effective spin shift into the index computation, we obtain exact closed-form expressions for the line defect half-indices which are Askey-Wilson type moments.