Maths HEP Lunchtime Seminars: A very-algebraic approach to gauged maximal supergravities
26 February 2010 13:00 in CM221
We give a method of deriving the field-strengths of all massless and massive, i.e. gauged, maximal supergravity theories, in any dimension starting from the very-extended Kac-Moody algebra E(11). Considering the subalgebra of E(11) 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. This extension is not compatible with the full E(11) algebra, which implies that E(11) is not a symmetry of maximal supergravity theories. Given the enlarged algebra corresponding to the massless theory, we show that this can be deformed to obtain the algebra corresponding to the gauged theory. We show how this works in detail for the case of Scherk-Schwarz reduction of IIB to nine dimensions. We then show how the same method can be applied to derive the gauged IIA theory that results from the gauging of the scaling symmetry. We finally classify all the possible deformations in any dimensions and show that these are in one to one correspondence with all the possible gauged supergravities. This includes also the gauging of the scaling symmetry in any dimension.