Gauge Theories, Duality Relations and the Tensor Hierarchy

Details Gauge Theories, Duality Relations and the Tensor Hierarchy Gauge Theories, Duality Relations and the Tensor Hierarchy

2009-01-14

arxiv.org/abs/0901.2054v2

JHEP 0904:123,2009

Physics

High Energy Physics

High Energy Physics - Theory

48 pages, v2: number of clarifications, ref. added, to appear in JHEP

Scientific paper

10.1088/1126-6708/2009/04/123

We compute the complete 3- and 4-dimensional tensor hierarchies, i.e. sets of p-form fields, with $1\le p\le D$, which realize an off-shell algebra of bosonic gauge transformations. We show how these tensor hierarchies can be put on-shell by introducing a set of duality relations, thereby introducing additional scalars and a metric tensor. These so-called duality hierarchies encode the equations of motion of the bosonic part of the most general gauged supergravity theories in those dimensions, including the (projected) scalar equations of motion. We construct gauge-invariant actions that include all the fields in the tensor hierarchies. We elucidate the relation between the gauge transformations of the p-form fields in the action and those of the same fields in the tensor hierarchy.

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