Abstract
We study exactly marginal deformations of 3d \( \mathcal{N}=2 \) CFTs dual to AdS4 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 S7, Q1,1,1 and M1,1,1 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 γ-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.
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Ashmore, A. Marginal deformations of 3d \( \mathcal{N}=2 \) CFTs from AdS4 backgrounds in generalised geometry. J. High Energ. Phys. 2018, 60 (2018). https://doi.org/10.1007/JHEP12(2018)060
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DOI: https://doi.org/10.1007/JHEP12(2018)060