Tensor hierarchies, Borcherds algebras and E11

Details Tensor hierarchies, Borcherds algebras and E11 Tensor hierarchies, Borcherds algebras and E11

2011-10-21

arxiv.org/abs/1110.4892v2

JHEP 1202 (2012) 066

Physics

High Energy Physics

High Energy Physics - Theory

22 pages. v2: Published version (except for a few minor typos detected after the proofreading, which are now corrected)

Scientific paper

Gauge deformations of maximal supergravity in D=11-n dimensions generically give rise to a tensor hierarchy of p-form fields that transform in specific representations of the global symmetry group E(n). We derive the formulas defining the hierarchy from a Borcherds superalgebra corresponding to E(n). This explains why the E(n) representations in the tensor hierarchies also appear in the level decomposition of the Borcherds superalgebra. We show that the indefinite Kac-Moody algebra E(11) can be used equivalently to determine these representations, up to p=D, and for arbitrarily large p if E(11) is replaced by E(r) with sufficiently large rank r.

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