Gauged supergravities from M-theory reductions

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Regular Article - Theoretical Physics


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 M7, 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 M8 over M7. The non-harmonic forms we propose are the ones contained in one of the Kohn-Rossi cohomology groups, which is finite-dimensional 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 M6, or in terms of Milnor cycles arising in deformations of M8. 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.


Differential and Algebraic Geometry Flux compactifications Supergravity Models Superstring Vacua 


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This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.


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© The Author(s) 2018

Authors and Affiliations

  1. 1.Institut de Physique Théorique, Université Paris Saclay, CEA, CNRSGif sur YvetteFrance
  2. 2.Instituut voor Theoretische FysicaKatholieke Universiteit LeuvenLeuvenBelgium
  3. 3.Dipartimento di FisicaUniversità di Milano-BicoccaMilanoItaly
  4. 4.INFN — Sezione di Milano-BicoccaMilanoItaly

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