Supersymmetric Three-Form Flux Perturbations on AdS₅

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We consider warped type IIB supergravity solutions with three-form flux and N=1 supersymmetry, which arise as the supergravity duals of confining gauge theories. We first work in a perturbation expansion around AdS₅ × S⁵, as in the work of Polchinski and Strassler, and from the N=1 conditions and the Bianchi identities recover their first-order solution generalized to an arbitrary 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.