5d gauge theories on orbifolds and 4d 't Hooft line indices

TL;DR

This paper investigates the relationship between 5d gauge theory indices on orbifolds and 4d 't Hooft line indices, revealing a connection to instanton moduli spaces and monopole bubbling phenomena.

Contribution

It demonstrates that 5d indices on orbifolds approach 4d 't Hooft line indices in the large orbifold limit and uncovers a link to instanton moduli space Hilbert series.

Findings

Indices become 4d in the large orbifold limit

Non-perturbative index aspects relate to monopole bubbling

Connection established between monopole bubbling indices and instanton Hilbert series

Abstract

We study indices for 5d gauge theories on S^1 \times S^4/Z_n. In the large orbifold limit, n \rightarrow \infty, we find evidence that the indices become 4d indices in the presence of a 't Hooft line operator. The non-perturbative part of the index poses some subtleties when being compared to the 4d monopole bubbling which happens in the presence of 't Hooft line operators. We study such monopole bubbling indices and find an interesting connection to the Hilbert series of the moduli space of instantons on an auxiliary ALE space.