The vanishing volume of D = 4 superspace

The volume of on-shell D = 4, superspace is shown to vanish. Despite this, it is shown that there is a fully supersymmetric and duality-invariant candidate ∇8R4 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 ∇6R4 invariant. Similar results are derived for .

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