Surface defects in E-string compactifications and the van Diejen model

TL;DR

This paper explores the supersymmetric index of 4D theories from E string compactifications, deriving a difference operator related to van Diejen's model that introduces surface defects.

Contribution

It introduces a novel difference operator for surface defects in E string compactifications, connecting supersymmetric indices to van Diejen's analytic difference operator.

Findings

Derived the difference operator for surface defects in E string compactifications.

Connected the operator to van Diejen's analytic difference operator.

Enhanced understanding of surface defects in 4D supersymmetric theories.

Abstract

We study the supersymmetric index of four dimensional theories obtained by compactifications of the six dimensional E string theory on a Riemann surface. In particular we derive the difference operator introducing certain class of surface defects to the index computation. The difference operator turns out to be, up to a constant shift, an analytic difference operator discussed by van Diejen.