<p>We construct and analyse holographic duals to a class of four-dimensional <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_27005_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="MATHML"><math display="inline"> <mi mathvariant="script">N</mi> </math></EquationSource> <EquationSource Format="TEX">\( \mathcal{N} \)</EquationSource> </InlineEquation> = 1 SU(<i>N</i><sub><i>c</i></sub>) 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 <i>N</i><sub><i>f</i></sub> fundamental flavours. The U(1) R-symmetry is anomaly-free only if <i>N</i><sub><i>f</i></sub> = 2<i>N</i><sub><i>c</i></sub>. We implement a supersymmetric twisted-circle reduction, holographically realised through a smoothly shrinking S<sup>1</sup> fibered over the internal U(1)<sub>R</sub> direction. We obtain new regular type IIB supergravity backgrounds that are valid only if the condition <i>N</i><sub><i>f</i></sub> = 2<i>N</i><sub><i>c</i></sub> 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 <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_27005_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="MATHML"><math display="inline"> <mi mathvariant="script">N</mi> </math></EquationSource> <EquationSource Format="TEX">\( \mathcal{N} \)</EquationSource> </InlineEquation> = 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.</p>

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Twisted-circle compactifications of SQCD-like theories and holography

  • Niall T. Macpherson,
  • Paul Merrikin,
  • Carlos Nunez,
  • Ricardo Stuardo

摘要

We construct and analyse holographic duals to a class of four-dimensional N \( \mathcal{N} \) = 1 SU(Nc) 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 Nf fundamental flavours. The U(1) R-symmetry is anomaly-free only if Nf = 2Nc. We implement a supersymmetric twisted-circle reduction, holographically realised through a smoothly shrinking S1 fibered over the internal U(1)R direction. We obtain new regular type IIB supergravity backgrounds that are valid only if the condition Nf = 2Nc 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 N \( \mathcal{N} \) = 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.