Minimal $D=4$ $\mathcal{N}=2$ supergravity from $D=11$: An M-theory free lunch

Abstract

We present a new consistent truncation of $D=11$ supergravity to $D=4$ $\mathcal{N}=2$ minimal gauged supergravity, on the seven-dimensional internal Riemannian space corresponding to the most general class of $D=11$ solutions with an AdS${}_4$ factor and $\mathcal{N}=2$ supersymmetry. A truncation ansatz is proposed and its consistency checked at the level of the $D=11$ Bianchi identity, bosonic equations of motion, and supersymmetry variations of the gravitino. The general class includes an $\mathcal{N}=2$ AdS${}_4$ solution dual to the conformal, low-energy physics phase corresponding to a mass deformation of the M2-brane field theory. A consistent truncation recently constructed on this particular geometry is recovered from our formalism.

v2: Minor change of title, new paragraph in the discussion section and references added. Version to be published in JHEP