Superconformal indices on $S^1\times (S^5/Z_p)$

TL;DR

This paper computes superconformal indices for 6d theories on a specific orbifolded space, analyzing their behavior under squashing, temperature variations, and S-duality, revealing smooth limits and duality exchanges.

Contribution

It introduces generating functions for abelian superconformal indices on $S^1\times (S^5/Z_p)$, exploring their properties and dualities in detail.

Findings

Superconformal indices are smooth in the unsquashed limit.

High and low temperature behaviors of the indices are characterized.

S-duality exchanges the Hopf and temporal circles in the large p limit.

Abstract

We obtain generating functions associated to the abelian superconformal indices for 6d $(1,0)$ tensor and hypermultiplets on $S^1\times (S^5/Z_p)$. We extract the superconformal indices and their high and low temperature behaviors. We consider round and generically squashed $S^5$ in turn. We show that the unsquashed limit of the superconformal indices is smooth. We examine S-duality in the large $p$ limit that acts by exchanging the Hopf circle with the temporal circle.