The vanishing volume of D=4 superspace
Abstract
The volume of on-shell D=4, N=8 superspace is shown to vanish. Despite this, it is shown that there is a fully supersymmetric and duality-invariant candidate d8 R4 counterterm corresponding to an anticipated seven-loop logarithmic divergence in D=4. We construct this counterterm explicitly and also give the complete nonlinear extension of the 1/8-BPS d6 R4 invariant. Similar results are derived for N=4,5 & 6.
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