Twisted-Circle Compactifications of SQCD-like Theories and Holography

TL;DR

This paper constructs holographic duals for N=1 SQCD-like theories compactified on a circle with an R-symmetry twist, revealing a consistent 3D gapped phase only when the number of flavors equals twice the number of colors.

Contribution

It introduces new regular type IIB supergravity backgrounds for twisted circle compactifications of SQCD-like theories, linking anomaly cancellation to geometric regularity.

Findings

Valid backgrounds only if N_f = 2N_c

Emergence of a 3D N=2 gapped phase

Consistent holographic observables matching field theory expectations

Abstract

We construct and analyse holographic duals to a class of four-dimensional N = 1 SU($N_c$) SQCD-like theories compactified on a circle with an R-symmetry twist. The setup originates from type IIB backgrounds previously proposed as duals to SQCD with $N_f$ fundamental flavours. The U(1) R-symmetry is anomaly-free only if $ N_f = 2N_c$. We implement a supersymmetric twisted-circle reduction, holographically realised through a smoothly shrinking $S^1$ fibered over the internal U(1)$_R$ direction. We obtain new regular type IIB supergravity backgrounds that are valid only if the condition $N_f = 2N_c$ is satisfied--mirroring the anomaly cancellation requirement in the field theory. We compute various field-theoretic observables--including the Chern-Simons level, Wilson loop and the holographic central charge--showing the emergence of a 3D ${\cal N} = 2$ gapped phase consistent with a Chern-Simons TQFT. This work highlights the interplay between anomalies, supersymmetry, and geometry in the holographic realisation of compactified gauge theories with fundamental matter.