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High Energy Physics - Theory, hep-th
Abstract:
The role of duality symmetries in the construction of counterterms for
maximal supergravity theories is discussed in a field-theoretic context from
different points of view. These are: dimensional reduction, the question of
whether appropriate superspace measures exist and information about non-linear
invariants that can be gleaned from linearised ones. In D=4, N=8 supergravity
we find that all three of these arguments suggest that F-term counterterms
cannot be E7(7)-invariant and that the theory should be finite up to seven
loops as a consequence. We also argue that N=6 supergravity is finite at three
and four loops and that N=5 supergravity should be three-loop finite.
