Loop and surface operators in N=2 gauge theory and Liouville modular geometry

TL;DR

This paper explores the duality between Liouville theory and N=2 gauge theory, focusing on how surface and line operators correspond across the duality, and computes their expectation values.

Contribution

It establishes a mapping of surface and line operators in N=2 gauge theories to Liouville theory operators and computes their expectation values.

Findings

Mapped surface and line operators between gauge theory and Liouville theory.

Computed expectation values of supersymmetric line operators in various N=2 gauge theories.

Enhanced understanding of extended objects in gauge theory via duality.

Abstract

Recently, a duality between Liouville theory and four dimensional N=2 gauge theory has been uncovered by some of the authors. We consider the role of extended objects in gauge theory, surface operators and line operators, under this correspondence. We map such objects to specific operators in Liouville theory. We employ this connection to compute the expectation value of general supersymmetric 't Hooft-Wilson line operators in a variety of N=2 gauge theories.