Supersymmetry counterterms revisited

TL;DR

This paper revisits supersymmetry counterterms, showing how harmonic superspace improves divergence estimates and aligning them with recent unitarity calculations, with implications for supergravity divergence onset.

Contribution

It demonstrates that harmonic superspace refines divergence estimates in supersymmetric theories, aligning them with recent unitarity results and suggesting higher loop orders for divergences in supergravity.

Findings

Harmonic superspace improves divergence estimates.

Estimates agree with recent unitarity calculations.

Potential six-loop divergence in N=8 supergravity.

Abstract

Superspace power-counting rules give estimates for the loop order at which divergences can first appear in non-renormalisable supersymmetric field theories. In some cases these estimates can be improved if harmonic superspace, rather than ordinary superspace, is used. The new estimates are in agreement with recent results derived from unitarity calculations for maximally supersymmetric Yang-Mills theories in five and six dimensions. For N=8 supergravity in four dimensions, we speculate that the onset of divergences may correspondingly occur at the six loop order.