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Spencer Cohomology and 11-Dimensional Supergravity

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http://link.springer.com/10.1007/s00220-016-2700-1
Original languageEnglish
Pages (from-to)627-660
Number of pages34
JournalCommunications in Mathematical Physics
Volume349
Issue number2
Early online date29 Jun 2016
DOIs
Publication statusPublished - Jan 2017

Abstract

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 ZZ -graded subalgebras h=h−2⊕h−1⊕h0h=h−2⊕h−1⊕h0 of the Poincaré superalgebra g=g−2⊕g−1⊕g0=V⊕S⊕so(V)g=g−2⊕g−1⊕g0=V⊕S⊕so(V) which differ only in zero degree, that is h0⊂g0h0⊂g0 and hj=gjhj=gj for j<0j<0 . Aside from the Poincaré superalgebra itself and its ZZ -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.

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