Ultraviolet divergences in maximal supergravity from a pure spinor point of view

TL;DR

This paper investigates ultraviolet divergences in maximal supergravity using pure spinor formalism, revealing a loop cutoff at six or seven loops depending on the amplitude, and clarifying the role of non-minimal variables.

Contribution

It introduces a refined analysis of divergences in supergravity with a new b-ghost and loop regularisation, updating previous field theory results.

Findings

Loop dependence cuts off at six loops for 4-point amplitudes.

Divergences are limited to seven loops in general.

Non-minimal variable r's degrees of freedom influence divergence behavior.

Abstract

The ultraviolet divergences of amplitude diagrams in maximal supergravity are investigated using the pure spinor superfield formalism in maximal supergravity, with maximally supersymmetric Yang-Mills theory for reference. We comment on the effects of the loop regularisation in relation to the actual absence of high powers (within the degrees of freedom) of the non-minimal variable r. The absence affects previous results of the field theory description, which is examined more closely (with a new b-ghost) with respect to the limit on the dimension for finiteness of the theory, dependent on the number of loops present. The results imply a cut-off of the loop dependence at six loops for the 4-point amplitude, and at seven loops otherwise.