Twisted-circle compactifications of SQCD-like theories and holography
Niall T. Macpherson, Paul Merrikin, Carlos Núñez, Ricardo Stuardo
Abstract
A bstract We construct and analyse holographic duals to a class of four-dimensional $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 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 = 2 N 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 = 2 N 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 $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 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.