| arXiv:0809.5034 (September 2008) |
| On the maximal superalgebras of supersymmetric backgrounds |
| José Figueroa-O'Farrill, Emily Hackett-Jones, George Moutsopoulos and Joan Simón | School of Mathematics and Maxwell Institute for Mathematical Sciences, University of Edinburgh, James Clerk Maxwell Building, King's Buildings, Edinburgh EH9 3JZ, UK
Departament de Física Teòrica & IFIC (CSIC-UVEG), Universitat de València, 46100 Burjassot, Spain
| | Received. 29 September 2008 Last updated. 29 September 2008 | | Abstract. In this note we give a precise definition of the notion of a maximal superalgebra of certain types of supersymmetric supergravity backgrounds, including the Freund-Rubin backgrounds, and propose a geometric construction extending the well-known construction of its Killing superalgebra. We determine the structure of maximal Lie superalgebras and show that there is a finite number of isomorphism classes, all related via contractions from an orthosymplectic Lie superalgebra. We use the structure theory to show that maximally supersymmetric waves do not possess such a maximal superalgebra, but that the maximally supersymmetric Freund-Rubin backgrounds do. We perform the explicit geometric construction of the maximal superalgebra of AdS_4 x S^7 and find that is isomorphic to osp(1|32). We propose an algebraic construction of the maximal superalgebra of any background asymptotic to AdS_4 x S^7 and we test this proposal by computing the maximal superalgebra of the M2-brane in its two maximally supersymmetric limits, finding agreement. | | Categories. hep-th | | Comment. 17 pages | | Report No. EMPG-08-15 |
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