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`Local E(11) and gauged maximal supergravities'

Abstract: 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 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. 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.
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