Chiral algebras, localization and surface defects

Yiwen Pan,Wolfger Peelaers

doi:10.1007/jhep02(2018)138

Abstract

Four-dimensional mathcal{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.

Highlights

The SCFT/chiral algebra correspondence was constructed algebraically in [1]: the relevant subsector of local operators was isolated by passing to the cohomology of either one of two well-chosen nilpotent supercharge Qi, i = 1, 2, and it was shown that the algebra of cohomology classes, obtained by reducing the operator product algebra, is isomorphic to a chiral algebra
The representation theory of the chiral algebras associated with N = 2 SCFTs can be probed by inserting surface defects in the four-dimensional theory [1, 21, 22]
In this paper we have used supersymmetric localization techniques to show that the chiral algebra associated with four-dimensional N = 2 superconformal quantum field theories is accessible directly in the path integral

Summary

Introduction

We map the theory to the round four-sphere, and employ supersymmetric localization techniques with respect to the supercharge Q = Q1 +Q2 to argue that the theory can be localized to a quantum field theory on a two-sphere.1 This quantum field theory is precisely the chiral algebra associated with the free hypermultiplet, namely the symplectic boson pair. W , the quantum fields Q and Q are pinned at the north pole and we collectively wrote φt2cd for the bottom components of the twisted chiral multiplets of the two-dimensional theory. The latter are set to their constant BPS profile (which is integrated/summed over).

Objectives

Results

Conclusion