Symmetry enhancements via 5d instantons, qW-algebrae and (1,0) superconformal index

TL;DR

This paper investigates 6d superconformal theories from M5-branes, showing how 5d instantons and pq-web dualities lead to symmetry enhancements and relations in qW-algebras, with exact partition functions matching 6d indices.

Contribution

It introduces a dual pq-web description of 6d theories, computes exact 5d partition functions, and reveals new relations among qW-algebra correlators derived from S-duality.

Findings

Exact 5d partition function matches 6d superconformal index.

pq-web S-duality implies new relations in qW-algebra correlators.

Spectrum of instanton operators drives symmetry enhancement.

Abstract

We explore N=(1,0) superconformal six-dimensional theories arising from M5-branes probing a transverse A_k singularity. Upon circle compactification to 5 dimensions, we describe this system with a dual pq-web of five-branes and propose the spectrum of basic five-dimensional instanton operators driving global symmetry enhancement. For a single M5-brane, we find that the exact partition function of the 5d quiver gauge theory matches the 6d (1,0) index, which we compute by letter counting. We finally show that S-duality of the pq-web implies new relations among vertex correlators of qW-algebrae.