Surface defects on E-string from 5-brane webs

TL;DR

This paper investigates surface defects in 6d E-string theory using geometric transitions and brane web diagrams, revealing how defects influence symmetry breaking and providing explicit partition functions.

Contribution

It introduces a novel method to compute surface defect partition functions for E-string theory via geometric transition and brane web analysis.

Findings

Partition functions for 5d SU(3) and Sp(2) gauge theories agree via duality.

Derived surface defect partition function for E-string on b4b4.

Showed how defects break global symmetry depending on their insertion.

Abstract

We study 6d E-string theory with defects on a circle. Our basic strategy is to apply the geometric transition to the supersymmetric gauge theories. First, we calculate the partition functions of the 5d SU(3)$_0$ gauge theory with 10 flavors, which is UV-dual to the 5d Sp(2) gauge theory with 10 flavors, based on two different 5-brane web diagrams, and check that two partition functions agree with each other. Then, by utilizing the geometric transition, we find the surface defect partition function for E-string on $\mathbb{R}^4\times T^2$. We also discuss that our result is consistent with the elliptic genus. Based on the result, we show how the global symmetry is broken by the defects, and discuss that the breaking pattern depends on where/how we insert the defects.