TY - JOUR

T1 - Kaluza-Klein reductions of maximally supersymmetric five-dimensional Lorentzian spacetimes

AU - Figueroa-O’Farrill, José

AU - Franchetti, Guido

N1 - 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).

PY - 2022/11/3

Y1 - 2022/11/3

N2 - 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.

AB - 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.

KW - differential and algebraic geometry

KW - space-time symmetries

KW - supergravity models

UR - http://www.scopus.com/inward/record.url?scp=85141684796&partnerID=8YFLogxK

U2 - 10.1088/1361-6382/ac9108

DO - 10.1088/1361-6382/ac9108

M3 - Article

AN - SCOPUS:85141684796

VL - 39

JO - Classical Quantum Gravity

JF - Classical Quantum Gravity

SN - 0264-9381

IS - 21

M1 - 215009

ER -