Geometric construction of Killing spinors and supersymmetry algebras in homogeneous spacetimes

Abstract

We show how the Killing spinors of some maximally supersymmetric supergravity solutions whose metrics describe symmetric spacetimes (including AdS, AdS × S and Hpp-waves) can be easily constructed using purely geometrical and group-theoretical methods. The calculation of the supersymmetry algebras is extremely simple in this formalism.

The near-horizon limit of the extreme rotating d 5 black hole as a homogeneous spacetime

“…Their Killing vectors and spinors and their relations that determine their supersymmetry algebras can be found by simple geometrical methods [1].…”

SU(1, 1|N) superconformal mechanics with fermionic gauge symmetry

“…Because the MC one-forms on the subgroup H transform as connections (see e.g. [41,42]), they can be used for building the Wess-Zumino (WZ) term [34]. More precisely, when the subgroup H decomposes into the product of…”

Rigid 4D N = 2 $$ \mathcal{N}=2 $$ supersymmetric backgrounds and actions

“…Of course, solutions that are only locally isomorphic to supercoset spaces may be available, too, for instance in terms of orbifolds of homogeneous spaces. Let us briefly review how the supercoset space construction works in practice and how it can be used to obtain explicit expressions for the metric and Killing spinors in particular (See for instance [23,24]). We can consider the reciprocal superalgebra of formal generators P a , Q α i ,Qα i satisfying the same commutation relations as…”

“…The Cartan-Maurer form can be expanded as earlier, recalling that the physical vielbein is given by the coefficients of P a so that 23) in terms of the 'round' vielbein E I defined by Ω = dt P 0 + E I T I . We can use the same coset representative as in the unsquashed case.…”