The Virtue of Defects in 4D Gauge Theories and 2D CFTs

TL;DR

This paper establishes a precise correspondence between topological defect operators in 2D Liouville/Toda CFTs and loop/domain wall operators in 4D N=2 gauge theories, providing exact partition functions and unifying different operator descriptions.

Contribution

It constructs the correspondence between defect operators in 2D CFTs and operators in 4D gauge theories, and proves the equivalence of topological defect and Verlinde loop operators in 2D.

Findings

Exact partition functions with defect operators computed in 4D gauge theories.

Demonstration that topological defect and Verlinde loop operators are equivalent in 2D CFTs.

Quantitative validation with independent gauge theory analysis.

Abstract

We advance a correspondence between the topological defect operators in Liouville and Toda conformal field theories - which we construct - and loop operators and domain wall operators in four dimensional N=2 supersymmetric gauge theories on S^4. Our computation of the correlation functions in Liouville/Toda theory in the presence of topological defect operators, which are supported on curves on the Riemann surface, yields the exact answer for the partition function of four dimensional gauge theories in the presence of various walls and loop operators; results which we can quantitatively substantiate with an independent gauge theory analysis. As an interesting outcome of this work for two dimensional conformal field theories, we prove that topological defect operators and the Verlinde loop operators are different descriptions of the same operators.