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- Title
Spencer Cohomology and 11-Dimensional Supergravity.
- Authors
Figueroa-O'Farrill, José; Santi, Andrea
- 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 $${{\mathbb{Z}}}$$ -graded subalgebras $${\mathfrak{h}=\mathfrak{h}_{-2} \oplus\mathfrak{h}_{-1} \oplus\mathfrak{h}_{0}}$$ of the Poincaré superalgebra $${\mathfrak{g}=\mathfrak{g}_{-2} \oplus\mathfrak{g}_{-1} \oplus\mathfrak{g}_{0}=V\oplus S\oplus \mathfrak{so}(V)}$$ which differ only in zero degree, that is $${\mathfrak{h}_0\subset\mathfrak{g}_0}$$ and $${\mathfrak{h}_\mathfrak{j}=\mathfrak{g}_\mathfrak{j}}$$ for $${\mathfrak{j}<0}$$ . Aside from the Poincaré superalgebra itself and its $${{\mathbb{Z}}}$$ -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.
- Subjects
COHOMOLOGY theory; SUPERGRAVITY; BOSONS; DEFORMATIONS (Mechanics); SUPERALGEBRAS
- Publication
Communications in Mathematical Physics, 2017, Vol 349, Issue 2, p627
- ISSN
0010-3616
- Publication type
Article
- DOI
10.1007/s00220-016-2700-1