2009/01/31 by Eric A. Bergshoeff, Eric Bergshoeff, Jelle Hartong +5 · 2 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Numerical methods for differential equations #hep-th
paper · pdf · doi:10.1088/1126-6708/2009/04/123
published as JHEP 0904:123,2009 · 48 pages, v2: number of clarifications, ref. added, to appear in JHEP
arxiv created 2009/04/28 · openalex publication_date 2009/04/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
We compute the complete 3- and 4-dimensional tensor hierarchies, i.e. sets of p-form fields, with 1≤ p≤ 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.