Chiral Algebras, Localization and Surface Defects

TL;DR

This paper demonstrates how localization techniques can be used to access the chiral algebra structure in 4d N=2 superconformal theories, including the effects of surface defects, providing new computational insights.

Contribution

It extends localization methods to include surface defects in 4d N=2 theories, revealing how they correspond to modules of the chiral algebra and enabling calculation of their structure constants.

Findings

Localization computes chiral algebra from the path integral on the four-sphere.

Surface defects are described as modules of the chiral algebra.

Results provide a new computational approach for chiral algebra structures in presence of defects.

Abstract

Four-dimensional N = 2 superconformal quantum field theories contain a subsector carrying the structure of a chiral algebra. Using localization techniques, we show for the free hypermultiplet that this structure can be accessed directly from the path integral on the four-sphere. We extend the localization computation to include supersymmetric surface defects described by a generic 4d/2d coupled system. The presence of a defect corresponds to considering a module of the chiral algebra: our results provide a calculational window into its structure constants.