The Superconformal Index of Class S Theories of Type D

TL;DR

This paper computes the superconformal index of class S theories of type D, revealing a 2D topological quantum field theory structure and incorporating twist lines related to the Z_2 automorphism.

Contribution

It identifies the 2D TQFT that calculates the superconformal index for D-type class S theories, including effects of twist lines and automorphisms.

Findings

Determined the 2D TQFT for the superconformal index

Incorporated twist lines associated with Z_2 automorphism

Provided explicit computation for a parameter slice (p=0, q, t)

Abstract

We consider the superconformal index of class S theories of type D, which arise by compactification of the (2,0) D_n theories on a punctured Riemann surface C. We also allow for the presence of twist lines on C associated to the Z_2 outer automorphism of D_n. For a two-parameter slice (p=0, q, t) in the space of superconformal fugacities, we determine the 2d TQFT that computes the index.