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Generalized Kähler Potentials from Supergravity

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Abstract

We consider supersymmetric \({\mathcal{N} = 2}\) solutions with non–vanishing NS three–form. Building on worldsheet results, we reduce the problem to a single generalized Monge–Ampère equation on the generalized Kähler potential K recently interpreted geometrically by Lindström, Roček, 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 β–deformed \({\mathcal{N} = 4}\) super–Yang–Mills falls in our class.

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Authors and Affiliations

  1. Enrico Fermi Institute, University of Chicago, Chicago, IL, 60637, USA

    Nick Halmagyi

  2. ITP, Stanford University, Stanford, CA, 94305-4060, USA

    Alessandro Tomasiello

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  1. Nick Halmagyi
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  2. Alessandro Tomasiello
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Correspondence to Alessandro Tomasiello.

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Communicated by G. W. Gibbons

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Halmagyi, N., Tomasiello, A. Generalized Kähler Potentials from Supergravity. Commun. Math. Phys. 291, 1–30 (2009). https://doi.org/10.1007/s00220-009-0881-6

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