Kaluza-Klein reductions of maximally supersymmetric five-dimensional Lorentzian spacetimes

José Figueroa-O’Farrill, Guido Franchetti

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1 Citation (SciVal)


A recent study of filtered deformations of (graded subalgebras of) the minimal five-dimensional Poincaré superalgebra resulted in two classes of maximally supersymmetric spacetimes. One class are the well-known maximally supersymmetric backgrounds of minimal five-dimensional supergravity, whereas the other class does not seem to be related to supergravity. This paper is a study of the Kaluza-Klein (KK) reductions to four dimensions of this latter class of maximally supersymmetric spacetimes. We classify the Lorentzian and Riemannian KK reductions of these backgrounds, determine the fraction of the supersymmetry preserved under the reduction and in most cases determine explicitly the geometry of the four-dimensional quotient. Among the many supersymmetric quotients found, we highlight a number of novel non-homogeneous four-dimensional Lorentzian spacetimes admitting N = 1 supersymmetry, whose supersymmetry algebra is not a filtered deformation of any graded subalgebra of the four-dimensional N = 1 Poincaré superalgebra. Any of these four-dimensional Lorentzian spacetimes may serve as the arena for the construction of new rigidly supersymmetric field theories.

Original languageEnglish
Article number215009
JournalClassical and Quantum Gravity
Issue number21
Early online date1 Nov 2022
Publication statusPublished - 3 Nov 2022

Bibliographical note

Funding Information:
GF would like to thank the Simons Foundation for its support under the Simons Collaboration on Special Holonomy in Geometry, Analysis and Physics (Grant 488631).


  • differential and algebraic geometry
  • space-time symmetries
  • supergravity models

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)


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