Marginal deformations of 3d $\mathcal{N}=2$ CFTs from AdS${}_4$ backgrounds in generalised geometry

Abstract

We study exactly marginal deformations of 3d $\mathcal{N}=2$ CFTs dual to AdS${}_4$ solutions in eleven-dimensional supergravity using generalised geometry. Focussing on Sasaki-Einstein backgrounds, we find that marginal deformations correspond to turning on a four-form flux on the internal space at first order. Viewing this as the deformation of a generalised structure, we derive a general expression for the four-form flux in terms of a holomorphic function. We discuss the explicit examples of S${}^7$, Q${}^{1,1,1}$ and M${}^{1,1,1}$ and, using an obstruction analysis, find the conditions for the first-order deformations to extend all orders, thus identifying which marginal deformations are exactly marginal. We also show how the all-orders $\gamma$-deformation of Lunin and Maldacena can be encoded as a tri-vector deformation in generalised geometry and outline how to recover the supergravity solution from the generalised metric.

arXiv comment37 pages; references added in v3

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• Tri-vector deformations in $d=11$ supergravity
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• Global Properties of the Conformal Manifold for S-Fold Backgrounds
• Heterotic backgrounds via generalised geometry: moment maps and moduli
• Marginal deformations and RG flows for type IIB S-folds
• Currents, charges and algebras in exceptional generalised geometry
• Black holes and general Freudenthal transformations
• Marginal deformations from type IIA supergravity
• Tri-vector deformations on compact isometries
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• Charting the Conformal Manifold of Holographic CFT${}_2$'s
• SUSY and tri-vector deformations
• Higher curvature Bianchi identities, generalised geometry and $L_{\infty }$ algebras
• Tri-vector deformations with external fluxes