2009/02/28 by Fabio Riccioni, Peter West
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Quantum Chromodynamics and Particle Interactions #hep-th
paper · pdf · doi:10.1088/1126-6708/2009/04/051
published as JHEP 0904:051,2009 · LaTeX file, 71 pages, 5 figures, references added, typos corrected
arxiv created 2009/03/16 · openalex publication_date 2009/04/14 · arxiv updated 2009/12/01 · openalex created_date 2016/07/22 · openalex updated_date 2026/08/01
We give a method of deriving the field-strengths of all massless and massive maximal supergravity theories in any dimension starting from the Kac-Moody algebra E11. Considering the subalgebra of E11 that acts on the fields in the non-linear realisation as a global symmetry, we show how this is promoted to a gauge symmetry enlarging the algebra by the inclusion of additional generators. We show how this works in eleven dimensions, and we call the resulting enlarged algebra E11local. Torus reduction to D dimensions corresponds to taking a subalgebra of E11local, called E11,Dlocal, that encodes the full gauge algebra of the corresponding D-dimensional massless supergravity. We show that each massive maximal supergravity in D dimensions is a non-linear realisation of an algebra E11,Dlocal. We show how this works in detail for the case of Scherk-Schwarz reduction of IIB to nine dimensions, and in particular we show how E11,9local arises as a subalgebra of the algebra E11,10Blocal associated to the ten-dimensional IIB theory. This subalgebra corresponds to taking a combination of generators which is different to the massless case. We then show that E11,Dlocal appears as a deformation of the massless algebra E11,Dlocal in which the commutation relations between the E11 and the additional generators are modified. We explicitly illustrate how the deformed algebra is constructed in the case of massive IIA and of gauged five-dimensional supergravity. These results prove the naturalness and power of the method.