Surface Defects in E-String Compactifications and the van Diejen Model

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 a 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.