Killing superalgebras for lorentzian five-manifolds
arXiv:2105.05775 · doi:10.1007/JHEP07(2021)209
Abstract
We calculate the relevant Spencer cohomology of the minimal Poincaré superalgebra in 5 spacetime dimensions and use it to define Killing spinors via a connection on the spinor bundle of a 5-dimensional lorentzian spin manifold. We give a definition of bosonic backgrounds in terms of this data. By imposing constraints on the curvature of the spinor connection, we recover the field equations of minimal (ungauged) 5-dimensional supergravity, but also find a set of field equations for an -valued one-form which we interpret as the bosonic data of a class of rigid supersymmetric theories on curved backgrounds. We define the Killing superalgebra of bosonic backgrounds and show that their existence is implied by the field equations. The maximally supersymmetric backgrounds are characterised and their Killing superalgebras are explicitly described as filtered deformations of the Poincaré superalgebra.
arXiv comment29 pages; LaTex errors on pages 26 and 27 fixed in v2. v3 final version to appear in JHEP
References in corpus (16)
- All supersymmetric solutions of minimal supergravity in five dimensions
- D--branes and Spinning Black Holes
- Rigid Supersymmetric Theories in Curved Superspace
- Localization techniques in quantum field theories
- Supersymmetry and homogeneity of M-theory backgrounds
- On the supersymmetries of anti de Sitter vacua
- Killing Spinors and SYM on Curved Spaces
- A Small Note on PP-Wave Vacua in 6 and 5 Dimensions
- The homogeneity theorem for supergravity backgrounds
- Supergravity vacua and lorentzian Lie groups
- Killing superalgebras for Lorentzian four-manifolds
- Spencer cohomology and eleven-dimensional supergravity
- Eleven-dimensional supergravity from filtered subdeformations of the Poincaré superalgebra
- Killing superalgebras for Lorentzian six-manifolds
- Kinematical superspaces
- Generalized Spencer Cohomology and filtered Deformations of Z-graded Lie Superalgebras