Modified elliptic gamma functions and 6d superconformal indices

TL;DR

This paper introduces a modified elliptic gamma function suitable for certain parameter regimes and applies it to compute superconformal indices of 6d theories with 4d defects, revealing W(E7) symmetry.

Contribution

It constructs a modified double elliptic gamma function valid on the unit circle and applies it to superconformal indices of 6d theories with novel symmetry properties.

Findings

The modified gamma function is well-defined on the unit circle.

The superconformal index exhibits W(E7) symmetry.

The model links 6d hypermultiplets with 4d defect theories.

Abstract

We construct a modified double elliptic gamma function which is well defined when one of the base parameters lies on the unit circle. A model consisting of 6d hypermultiplets coupled to a gauge field theory living on a 4d defect is proposed whose superconformal index uses the double elliptic gamma function and obeys W(E7)-group symmetry.