A duality web of linear quivers

TL;DR

This paper uncovers a complex web of dualities among supersymmetric linear quiver theories by applying the Bailey lemma to elliptic hypergeometric integrals, revealing new equivalences and constructions within Seiberg duality.

Contribution

It introduces a novel connection between elliptic hypergeometric integrals and dualities in supersymmetric quiver theories, expanding the understanding of Seiberg duality webs.

Findings

Equivalence of superconformal indices for different quivers

Construction of electric and magnetic theories via s-confining theories

Enlargement of duality web through Bailey lemma applications

Abstract

We show that applying the Bailey lemma to elliptic hypergeometric integrals on the $A_n$ root system leads to a large web of dualities for $\mathcal{N} = 1$ supersymmetric linear quiver theories. The superconformal index of Seiberg's SQCD with $SU(N_c)$ gauge group and $SU(N_f)\times SU(N_f)\times U(1)$ flavour symmetry is equal to that of $N_f-N_c-1$ distinct linear quivers. Seiberg duality further enlarges this web by adding new quivers. In particular, both interacting electric and magnetic theories with arbitrary $N_c$ and $N_f$ can be constructed by quivering an $s$-confining theory with $N_f=N_c+1$.