2016/05/31 by Paul de Medeiros, José Figueroa-O’Farrill, José Figueroa-O'Farrill +1
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebra over a field #Black Holes and Theoretical Physics #Cohomology #Dimension (graph theory) #Killing spinor #Lie superalgebra #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Physics #Pure mathematics #Spinor #Subalgebra #Superalgebra #Supergravity #Supermatrix #Supersymmetry #Supersymmetry algebra #hep-th #math.DG #math.RT
paper · pdf · doi:10.1007/jhep06(2016)106
published as J. High Energy Phys. 6 (2016), 2016:106 (50 pp) · 36 pages (v2: final version to appear in JHEP)
openalex publication_date 2016/06/01 · arxiv created 2016/06/15 · arxiv updated 2016/07/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We determine the Killing superalgebras underpinning field theories with rigid unextended supersymmetry on Lorentzian four-manifolds by re-interpreting them as filtered deformations of ℤ -graded subalgebras with maximum odd dimension of the N = 1 Poincaré superalgebra in four dimensions. Part of this calculation involves computing a Spencer cohomology group which, by analogy with a similar result in eleven dimensions, prescribes a notion of Killing spinor, which we identify with the defining condition for bosonic supersymmetric backgrounds of minimal off-shell supergravity in four dimensions. We prove that such Killing spinors always generate a Lie superalgebra, and that this Lie superalgebra is a filtered deformation of a subalgebra of the N = 1 Poincaré superalgebra in four dimensions. Demanding the flatness of the connection defining the Killing spinors, we obtain equations satisfied by the maximally supersymmetric backgrounds. We solve these equations, arriving at the classification of maximally supersymmetric backgrounds whose associated Killing superalgebras are precisely the filtered deformations we classify in this paper.