2015/02/27 by Paul Howe, Jakob Palmkvist · 20 citations
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Affine Lie algebra #Algebra over a field #Algebraic number #Algebraic structure #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Computer science #Current algebra #Embedding #Hierarchy #Lie superalgebra #Mathematical analysis #Mathematical physics #Mathematics #Pure mathematics #Superalgebra #Superconformal algebra #Supergravity #Superspace #Supersymmetry #Supersymmetry algebra #Tensor (intrinsic definition) #Type (biology) #hep-th
paper · pdf · doi:10.1007/jhep05(2015)032
published in Journal of High Energy Physics 2015(5) (Springer Nature) · 59 pages, 1 figure
arxiv created 2015/02/27 · openalex publication_date 2015/05/01 · arxiv updated 2015/06/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
The forms in D-dimensional (half-)maximal supergravity theories are discussed for 3 ≤ D ≤ 11. Superspace methods are used to derive consistent sets of Bianchi identities for all the forms for all degrees, and to show that they are soluble and fully compatible with supersymmetry. The Bianchi identities determine Lie superalgebras that can be extended to Borcherds superalgebras of a special type. It is shown that any Borcherds superalgebra of this type gives the same form spectrum, up to an arbitrary degree, as an associated Kac-Moody algebra. For maximal supergravity up to D-form potentials, this is the very extended Kac-Moody algebra E 11. It is also shown how gauging can be carried out in a simple fashion by deforming the Bianchi identities by means of a new algebraic element related to the embedding tensor. In this case the appropriate extension of the form algebra is a truncated version of the so-called tensor hierarchy algebra.