# Surface Defects and Chiral Algebras

## TL;DR

This paper explores the relationship between superconformal surface defects in 4D N=2 theories and their associated chiral algebras, providing explicit index computations and connecting algebraic operations to defect constructions.

## Contribution

It introduces a framework linking surface defects to modules of chiral algebras and computes defect indices in specific theories, confirming theoretical predictions.

## Key findings

- Computed defect indices in free hypermultiplet and Argyres-Douglas theories
- Established correspondence between algebraic operations and defect constructions
- Confirmed agreement with predicted chiral algebra characters

## Abstract

We investigate superconformal surface defects in four-dimensional N=2 superconformal theories. Each such defect gives rise to a module of the associated chiral algebra and the surface defect Schur index is the character of this module. Various natural chiral algebra operations such as Drinfeld-Sokolov reduction and spectral flow can be interpreted as constructions involving four-dimensional surface defects. We compute the index of these defects in the free hypermultiplet theory and Argyres-Douglas theories, using both infrared techniques involving BPS states, as well as renormalization group flows onto Higgs branches. In each case we find perfect agreement with the predicted characters.