<p>We use the AdS/CFT correspondence to explicitly calculate some of the three-point functions in the planar limit of the 4d <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_27167_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 Leigh-Strassler SCFT. This strongly interacting CFT can be obtained as a mass deformation of the 4d <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_27167_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> = 4 SYM theory and admits a dual description in terms of an AdS<sub>5</sub> background of type IIB supergravity. Our analysis is based on the existence of a consistent truncation of the 10d supergravity to a tractable 5d gravitational theory with 10 scalar fields dual to some of the low-lying operators in the spectrum of the LS SCFT. We apply standard holographic techniques to this 10-scalar model to analytically calculate the correlators of interest and thus provide a rare example of explicit three-point functions of scalar non-BPS operators in strongly coupled 4d CFTs. Using superconformal Ward identities we perform several consistency checks of these holographic correlators. As a byproduct of our analysis we discuss some subtleties related to the calculation of extremal correlators in AdS/CFT and the contribution of scalar derivative couplings to the evaluation of Witten diagrams. Our work provides a blueprint for the holographic calculation of other correlators in the LS SCFT and similar top-down holographic models.</p>

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Holographic correlators beyond maximal supersymmetry

  • Nikolay Bobev,
  • Hynek Paul

摘要

We use the AdS/CFT correspondence to explicitly calculate some of the three-point functions in the planar limit of the 4d N \( \mathcal{N} \) = 1 Leigh-Strassler SCFT. This strongly interacting CFT can be obtained as a mass deformation of the 4d N \( \mathcal{N} \) = 4 SYM theory and admits a dual description in terms of an AdS5 background of type IIB supergravity. Our analysis is based on the existence of a consistent truncation of the 10d supergravity to a tractable 5d gravitational theory with 10 scalar fields dual to some of the low-lying operators in the spectrum of the LS SCFT. We apply standard holographic techniques to this 10-scalar model to analytically calculate the correlators of interest and thus provide a rare example of explicit three-point functions of scalar non-BPS operators in strongly coupled 4d CFTs. Using superconformal Ward identities we perform several consistency checks of these holographic correlators. As a byproduct of our analysis we discuss some subtleties related to the calculation of extremal correlators in AdS/CFT and the contribution of scalar derivative couplings to the evaluation of Witten diagrams. Our work provides a blueprint for the holographic calculation of other correlators in the LS SCFT and similar top-down holographic models.