Marginal deformations of 3d N=2 CFTs from AdS(4) backgrounds in generalised geometry

We study exactly marginal deformations of 3d 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,M-1,M-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 -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.