Supersymmetric dualities beyond the conformal window

TL;DR

The work tackles Seiberg-type dualities for 4D ${\\mathcal N}=1$ theories beyond the conformal window by leveraging the equalities of superconformal indices and elliptic hypergeometric integrals. It shows how restricting UV parameters (e.g., $UV=pq$) or setting $t=\\sqrt{pq}$ decouples fields and yields reduced electric and magnetic indices, producing multiple duals for ${SU(N)}$ and ${SP(2N)}$ outside the usual conformal window and sometimes with vanishing indices. The main contributions are explicit new duals outside the conformal window, including decoupled tensor sectors and extra $U(1)$ factors, and the observation that SC indices can vanish in these regimes, consistent with confinement scenarios. The results challenge the universality of the conformal window as a criterion for duality and motivate further work to classify all IR-duals of Seiberg-type SQCD and to understand how SC indices encode moduli spaces and superpotentials.

Abstract

Using the superconformal (SC) indices techniques, we construct Seiberg type dualities for $\mathcal{N}=1$ supersymmetric field theories outside the conformal windows. These theories are physically distinguished by the presence of chiral superfields with small or negative $R$-charges.