Aspects of line operators of class S theories

TL;DR

This paper explores the geometric representation and classification of line operators in class S theories, analyzing dualities, global gauge group forms, and discrete theta angles to reveal complex duality webs.

Contribution

It introduces a geometric interpretation of Wilson-'t Hooft line operators, classifies allowed line operators, and examines duality actions and their implications for gauge theories.

Findings

Identified geometric representation of line operators.

Classified line operators based on closure, locality, and maximality.

Revealed duality webs and the impact of global gauge group choices.

Abstract

Geometric picture of line operators of N=2 class S theories was found by imposing closure condition on operator product expansion (OPE) of line operators. In this paper, we first identify the geometric representation of ordinary Wilson-'t Hooft line operators of field theory, and study duality action on them. We further define a Dirac product between line operators and classify the allowed set of line operators by requiring: a: closure of OPE; b: mutual locality; c: maximality. Using above classifications, we find many distinct gauge theories associated with a single duality frame, and show explicitly that new possibilities correspond to the choice of global form of gauge group and discrete theta angles. We also study S and T duality actions relating those theories. In particular, we find very interesting duality webs for Maldacena-Nunez theory.