Kinematical superspaces

Abstract

We classify $N=1$ $d=4$ kinematical and aristotelian Lie superalgebras with spatial isotropy, but not necessarily parity nor time-reversal invariance. Employing a quaternionic formalism which makes rotational covariance manifest and simplifies many of the calculations, we find a list of $43$ isomorphism classes of Lie superalgebras, some with parameters, whose (nontrivial) central extensions are also determined. We then classify their corresponding simply-connected homogeneous $(4|4)$-dimensional superspaces, resulting in a list of $27$ homogeneous superspaces, some with parameters, all of which are reductive. We determine the invariants of low rank and explore how these superspaces are related via geometric limits.

50 pages, 5 figures, 14 tables (v2: final version to appear in JHEP)

References in corpus (11)

• On Schrödinger superalgebras
• Spatially isotropic homogeneous spacetimes
• Limits of three-dimensional gravity and metric kinematical Lie algebras in any dimension
• Geometry and BMS Lie algebras of spatially isotropic homogeneous spacetimes
• Kinematical Lie algebras via deformation theory
• Killing superalgebras for Lorentzian four-manifolds
• Kinematical superalgebras and Lie algebras of order 3
• Killing superalgebras for Lorentzian six-manifolds
• Conformal Lie algebras via deformation theory
• Possible Supersymmetric Kinematics
• Superization of Homogeneous Spin Manifolds and Geometry of Homogeneous Supermanifolds

Cited by in corpus (5)

• Carrollian manifolds and null infinity: A view from Cartan geometry
• Lie Algebra Expansion and Integrability in Superstring Sigma-Models
• Killing superalgebras for lorentzian five-manifolds
• Generalised Bargmann Superalgebras
• Kaluza-Klein reductions of maximally supersymmetric five-dimensional lorentzian spacetimes