Supersymmetric Three-Form Flux Perturbations on $AdS_5$

TL;DR

This paper explores supersymmetric three-form flux perturbations in type IIB supergravity, deriving first and second order solutions around $AdS_5 imes S^5$, and presents a family of exact solutions including the Klebanov--Strassler background.

Contribution

It generalizes first-order flux solutions to arbitrary ${ m N}=1$ superpotentials and finds exact solutions related to known supergravity backgrounds.

Findings

Derived first-order solutions consistent with ${ m N}=1$ conditions.

Computed second-order dilaton and axion fields.

Presented a family of exact solutions including Klebanov--Strassler.

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.