Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2009-06-05
JHEP 0909:095,2009
Physics
High Energy Physics
High Energy Physics - Theory
87 pages, 8 figures. Typos corrected, refs added, other minor changes. Version published on JHEP
Scientific paper
10.1088/1126-6708/2009/09/095
Starting from $E_{11}$ and the space-time translations we construct an algebra that promotes the global $E_{11}$ symmetries to local ones, and consider all its possible massive deformations. The Jacobi identities imply that such deformations are uniquely determined by a single tensor that belongs to the same representation of the internal symmetry group as the $D-1$ forms specified by $E_{11}$. The non-linear realisation of the deformed algebra gives the field strengths of the theory which are those of any possible gauged maximal supergravity theory in any dimension. All the possible deformed algebras are in one to one correspondence with all the possible massive maximal supergravity theories. The hierarchy of fields inherent in the $E_{11}$ formulation plays an important role in the derivation. The tensor that determines the deformation can be identified with the embedding tensor used previously to parameterise gauged supergravities. Thus we provide a very efficient, simple and unified derivation of the bosonic sector, and in the absence of gravity, of all maximal gauged supergravities from $E_{11}$.
Riccioni Fabio
Steele Duncan
West Peter
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