2015/11/30 by José Figueroa-O’Farrill, José Figueroa-O'Farrill, Andrea Santi · 1 citation
Mathematics · Physics and Astronomy · #Algebraic number #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Cohomology #Gravitino #Homotopy and Cohomology in Algebraic Topology #Lie superalgebra #Superalgebra #Supergravity #Supermatrix #Supersymmetry algebra #Zero (linguistics) #hep-th #math.DG #math.RT
paper · pdf · doi:10.1007/s00220-016-2700-1
published as Comm. Math. Phys. 349 (2017), 627-660 · 32 pages (v2: minor comments, reference added, final version to be published in CMP)
arxiv created 2016/05/13 · openalex created_date 2016/06/24 · openalex publication_date 2016/06/29 · arxiv updated 2017/04/10 · openalex updated_date 2026/08/05
We recover the classification of the maximally supersymmetric bosonic backgrounds of 11-dimensional supergravity by Lie algebraic means. We classify all filtered deformations of the ℤ -graded subalgebras \mathfrakh=\mathfrakh-2 ⊕\mathfrakh-1 ⊕\mathfrakh0 of the Poincaré superalgebra \mathfrakg=\mathfrakg-2 ⊕\mathfrakg-1 ⊕\mathfrakg0=V⊕ S⊕ \mathfrakso(V) which differ only in zero degree, that is \mathfrakh0⊂\mathfrakg0 and \mathfrakh_\mathfrakj=\mathfrakg_\mathfrakj for \mathfrakj<0 . Aside from the Poincaré superalgebra itself and its ℤ -graded subalgebras, there are only three other Lie superalgebras, which are the symmetry superalgebras of the non-flat maximally supersymmetric backgrounds. In passing we identify the gravitino variation with (a component of) a Spencer cocycle.