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

Understand

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.