On skein relations in class S theories

TL;DR

This paper explores skein relations in class S theories, detailing their role in network operators, and applies this understanding to specific theories like N=4 SU(3) super Yang-Mills and the T_3 theory.

Contribution

It provides a detailed description of skein relations in type A class S theories and applies this to explicit network constructions and superconformal index calculations.

Findings

Explicit networks for dyonic loops in N=4 SU(3) super Yang-Mills

Superconformal index computed for a network operator in T_3 theory

Detailed description of skein relations in class S theories of type A

Abstract

Loop operators of a class S theory arise from networks on the corresponding Riemann surface, and their operator product expansions are given in terms of the skein relations, that we describe in detail in the case of class S theories of type A. As two applications, we explicitly determine networks corresponding to dyonic loops of $N=4$ $SU(3)$ super Yang-Mills, and compute the superconformal index of a nontrivial network operator of the $T_3$ theory.