4d $\mathcal{N}=1$ quiver gauge theories and the $\mathrm{A_n}$ Bailey lemma

TL;DR

This paper explores the use of the Bailey lemma for elliptic hypergeometric integrals to identify new dualities and symmetry phenomena in four-dimensional $ ext{SU}(n+1)$ quiver gauge theories, supported by anomaly matching.

Contribution

It introduces a novel application of the $ ext{A}_n$ Bailey lemma to derive identities and dualities in $ ext{SU}(n+1)$ quiver gauge theories, linking mathematical identities to physical dualities.

Findings

Discovery of new dualities in $ ext{SU}(n+1)$ quiver gauge theories.

Identification of flavor symmetry breaking in SQCD.

Verification of 't Hooft anomaly matching conditions.

Abstract

We study the integral Bailey lemma associated with the $\mathrm{A_n}$-root system and identities for elliptic hypergeometric integrals generated thereby. Interpreting integrals as superconformal indices of four-dimensional $\mathcal{N}=1$ quiver gauge theories with the gauge groups being copies of $\mathrm{SU(n+1)}$, we provide evidence for various new dualities. Further confirmation is achieved by explicitly checking that the `t Hooft anomaly matching conditions holds. We discuss a flavour symmetry breaking phenomenon for supersymmetric quantum chromodynamics (SQCD), and by making use of the Bailey lemma we indicate its manifestation in a web of linear quivers dual to SQCD that exhibits full s-confinement.