Seiberg dualities and the 3d/4d connection

TL;DR

This paper explores the mathematical and physical connections between 4d and 3d supersymmetric gauge theories through dualities, proposing new identities and potential routes to understanding elusive 3d dualities.

Contribution

It introduces a new set of hypergeometric integral identities and suggests a novel approach to deriving 3d Seiberg dualities from 4d indices.

Findings

Derived non-standard degeneration identities for hyperbolic hypergeometric integrals.

Linked 4d superconformal indices to 3d dualities via degeneration limits.

Proposed a new method to approach 3d N=2 SQCD dualities.

Abstract

We discuss the degeneration limits of d=4 superconformal indices that relate Seiberg duality for the d=4 N=1 SQCD theory to Aharony and Giveon-Kutasov dualities for d=3 N=2 SQCD theories. On a mathematical level we argue that this 3d/4d connection entails a new set of non-standard degeneration identities between hyperbolic hypergeometric integrals. On a physical level we propose that such degeneration formulae provide a new route to the still illusive Seiberg dualities for d=3 N=2 SQCD theories with SU(N) gauge group.