Gauged supergravities from M-theory reductions

Abstract

In supergravity compactifications, there is in general no clear prescription on how to select a finite-dimensional family of metrics on the internal space, and a family of forms on which to expand the various potentials, such that the lower-dimensional effective theory is supersymmetric. We propose a finite-dimensional family of deformations for regular Sasaki-Einstein seven-manifolds M 7 , relevant for M-theory compactifications down to four dimensions. It consists of integrable Cauchy-Riemann structures, corresponding to complex deformations of the Calabi-Yau cone M 8 over M 7 . The non-harmonic forms we propose are the ones contained in one of the Kohn-Rossi cohomology groups, which is finitedimensional and naturally controls the deformations of Cauchy-Riemann structures. The same family of deformations can be also described in terms of twisted cohomology of the base M 6 , or in terms of Milnor cycles arising in deformations of M 8 . Using existing results on SU(3) structure compactifications, we briefly discuss the reduction of M-theory on our class of deformed Sasaki-Einstein manifolds to four-dimensional gauged supergravity.

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