Generalized Kaehler Potentials from Supergravity

TL;DR

This paper develops a method to find supersymmetric solutions in supergravity with non-zero NS three-form by reducing the problem to a generalized Monge-Ampere equation involving a generalized Kaehler potential, with applications to gauge/gravity duality.

Contribution

It introduces a new approach to derive supergravity solutions using a generalized Monge-Ampere equation linked to the Kaehler potential, extending previous worldsheet results.

Findings

Derived a generalized Monge-Ampere equation for supergravity solutions.

Applied the method to find a NS precursor of the Lunin-Maldacena background.

Connected the solutions to field theories with non-zero superpotential.

Abstract

We consider supersymmetric N=2 solutions with non-vanishing NS three-form. Building on worldsheet results, we reduce the problem to a single generalized Monge-Ampere equation on the generalized Kaehler potential K recently interpreted geometrically by Lindstrom, Rocek, Von Unge and Zabzine. One input in the procedure is a holomorphic function w that can be thought of as the effective superpotential for a D3 brane probe. The procedure is hence likely to be useful for finding gravity duals to field theories with non-vanishing abelian superpotential, such as Leigh-Strassler theories. We indeed show that a purely NS precursor of the Lunin-Maldacena dual to the beta-deformed N=4 super-Yang-Mills falls in our class.