Holographic Correlators Beyond Maximal Supersymmetry

TL;DR

This paper uses holographic duality to compute explicit three-point functions of scalar operators in a less supersymmetric 4d SCFT, providing new insights into strongly coupled gauge theories beyond maximal supersymmetry.

Contribution

It presents the first explicit holographic calculation of three-point functions of non-BPS scalar operators in a 4d SCFT with reduced supersymmetry, using a consistent truncation of supergravity.

Findings

Computed three-point functions of scalar operators in Leigh-Strassler SCFT

Validated results with superconformal Ward identities

Discussed subtleties in extremal correlator calculations

Abstract

We use the AdS/CFT correspondence to explicitly calculate some of the three-point functions in the planar limit of the 4d $\mathcal{N}=1$ Leigh-Strassler SCFT. This strongly interacting CFT can be obtained as a mass deformation of the 4d $\mathcal{N}=4$ SYM theory and admits a dual description in terms of an AdS$_5$ 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.