Pure spinor indications of ultraviolet finiteness in D=4 maximal supergravity

TL;DR

This paper uses pure spinor superfield theory to analyze potential divergences in D=4 maximal supergravity, providing evidence for its ultraviolet finiteness up to high loop orders.

Contribution

It extends previous pure spinor analyses to confirm the absence of divergences at seven and more loops, supporting the ultraviolet finiteness of D=4 supergravity.

Findings

No divergences at 7-loop 4-point amplitude

Ultraviolet finiteness in D=4 confirmed

Results align with other approaches

Abstract

The ultraviolet divergences of amplitude diagrams in maximal supergravity are characterised by a first possible divergence at seven loops for the 4-point amplitude (logarithmic) and, in its absence, at eight loops. We revisit the pure spinor superfield theory results of [arXiv:1412.5983], stating the absence of the divergence originating in the 4-point 7-loop amplitude as well as those of more than seven loops. The analysis, performed in terms of the one-particle irreducible loop structures giving rise to the divergences, is extended, especially with respect to the limits on the dimension for finiteness. The results correspond to those mentioned, known from other approaches, indicating an ultraviolet finiteness of maximal supergravity in D=4.