Supersymmetric Three-Form Flux Perturbations on $AdS_5$

TL;DR

This work constructs and analyzes supersymmetric three-form flux perturbations of the Type IIB background $AdS_5 \\times S^5$ to model confining gauge theories via gauge/gravity duality. By solving the ${\\mathcal N}=1$ supersymmetry conditions and Bianchi identities to first order around a Coulomb-branch D3-brane background, the authors show the perturbations are encoded by a holomorphic function $\\phi(z)$, interpreted as an arbitrary ${\\mathcal N}=1$ superpotential, plus a harmonic function $\\psi$ encoding higher-dimension operators; second-order dilaton/axion corrections are also derived. A simple class of exact solutions is presented, including the Klebanov-Strassler background, which emerges from a flux configuration tied to a harmonic 3-form on the transverse space and is related to Becker-Becker constructions in M theory. The results provide a structured route to explore nonconformal, confining holographic duals and connect well-known warped backgrounds within a unified supersymmetric framework.

Abstract

We consider warped type IIB supergravity solutions with three-form flux and ${\cal N}=1$ supersymmetry, which arise as the supergravity duals of confining gauge theories. We first work in a perturbation expansion around $AdS_5 \times S^5$, as in the work of Polchinski and Strassler, and from the ${\cal N}=1$ conditions and the Bianchi identities recover their first-order solution generalized to an arbitrary ${\cal N}=1$ superpotential. We find the second order dilaton and axion by the same means. We also find a simple family of exact solutions, which can be obtained from solutions found by Becker and Becker, and which includes the recent Klebanov--Strassler solution.