Surface defects and instanton partition functions

TL;DR

This paper develops a new method to compute superconformal indices and sphere partition functions of 4D and 5D supersymmetric theories with co-dimension two defects, validated by known results and dualities.

Contribution

It introduces a vortex-based prescription for defects in supersymmetric gauge theories, enabling systematic calculations of their indices and partition functions.

Findings

Validated the prescription against known results.

Established a computational strategy for defects via gauged linear sigma models.

Enhanced understanding of defect contributions in supersymmetric theories.

Abstract

We study the superconformal index of five-dimensional SCFTs and the sphere partition function of four-dimensional gauge theories with eight supercharges in the presence of co-dimension two half-BPS defects. We derive a prescription which is valid for defects which can be given a "vortex construction", i.e. can be defined by RG flow from vortex configurations in a larger theory. We test the prescription against known results and expected dualities. We employ our prescription to develop a general computational strategy for defects defined by coupling the bulk degrees of freedom to a Gauged Linear Sigma Model living in co-dimension two.