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arXiv · 1808.04981

A Generalised Garfinkle-Vachaspati Transform

Deepali Mishra·Yogesh K. Srivastava·Amitabh Virmani
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Abstract

The Garfinkle-Vachaspati transform is a deformation of a metric in terms of a null, hypersurface orthogonal, Killing vector $k^μ$. We explore a generalisation of this deformation in type IIB supergravity taking motivation from certain studies of the D1-D5 system. We consider solutions of minimal six-dimensional supergravity admitting null Killing vector $k^μ$ trivially lifted to type IIB supergravity by the addition of four-torus directions. The torus directions provide covariantly constant spacelike vectors $l^μ$. We show that the original solution can be deformed as $g_{μν} \to g_{μν} + 2 Φk_{(μ}l_{ν)}, C_{μν} \to C_{μν} - 2 Φk_{[μ}l_{ν]}$, provided the two-form supporting the original spacetime satisfies $i_k (dC) = - d k$, and where $Φ$ satisfies the equation of a minimal massless scalar field on the original spacetime. We show that the condition $i_k (dC) = - d k$ is satisfied by all supersymmetric solutions admitting null Killing vector. Hence all supersymmetric solutions of minimal six-dimensional supergravity can be deformed via this method. As an example of our approach, we work out the deformation on a class of D1-D5-P geometries with orbifolds. We show that the deformed spacetimes are smooth and identify their CFT description. Using Bena-Warner formalism, we also express the deformed solutions in other duality frames.

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Deepali Mishra, Yogesh K. Srivastava, Amitabh Virmani. 2018-08-15. A Generalised Garfinkle-Vachaspati Transform. https://doi.org/10.1007/s10714-018-2477-y

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