The vanishing volume of D=4 superspace

TL;DR

This paper demonstrates that the volume of on-shell D=4, N=8 superspace vanishes, yet a supersymmetric, duality-invariant counterterm related to a seven-loop divergence can be explicitly constructed, with similar results for other N values.

Contribution

It explicitly constructs a fully supersymmetric, duality-invariant counterterm for D=4, N=8 superspace, despite the superspace volume vanishing, and extends the analysis to N=4, 5, and 6.

Findings

Superspace volume in D=4, N=8 vanishes.

A fully supersymmetric, duality-invariant counterterm is constructed.

Results are extended to N=4, 5, and 6 cases.

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 d^8 R^4 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 d^6 R^4 invariant. Similar results are derived for N=4,5 & 6.