Supersymmetric Three-Form Flux Perturbations on $Ad{S}_5$

Abstract

We consider warped type IIB supergravity solutions with three-form flux and $\mathcal{N}=1$ supersymmetry, which arise as the supergravity duals of confining gauge theories. We first work in a perturbation expansion around $Ad{S}_5\times S^5$, as in the work of Polchinski and Strassler, and from the $\mathcal{N}=1$ conditions and the Bianchi identities recover their first-order solution generalized to an arbitrary $\mathcal{N}=1$ 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.

19 pages. reference added, minor clarifications. v3: reference to non-Abelian BPS monopole solution corrected (Chamseddine-Volkov)

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