A generalised Garfinkle-Vachaspati transform

DOI10.1007/S10714-018-2477-YzbMATH Open1409.83211arXiv1808.04981OpenAlexW2887909725WikidataQ128913635 ScholiaQ128913635MaRDI QIDQ1709992

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Publication date: 15 January 2019

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Abstract: The Garfinkle-Vachaspati transform is a deformation of a metric in terms of a null, hypersurface orthogonal, Killing vector $k^{m}u$. 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 $k^{m}u$ trivially lifted to type IIB supergravity by the addition of four-torus directions. The torus directions provide covariantly constant spacelike vectors $l^{m}u$. We show that the original solution can be deformed as $g_{muu}o{g}_{muu}+2Phi{k}_{(mu}{l}_{u)},C_{muu}o{C}_{muu}-2Phi{k}_{[mu}{l}_{u]}$, provided the two-form supporting the original spacetime satisfies $i_k(dC)=-dk$, and where $Phi$ satisfies the equation of a minimal massless scalar field on the original spacetime. We show that the condition $i_k(dC)=-dk$ 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.

Full work available at URL: https://arxiv.org/abs/1808.04981

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