Loop amplitudes in maximal supergravity with manifest supersymmetry

TL;DR

This paper develops a manifestly supersymmetric formalism for calculating amplitudes in maximal supergravity, revealing conditions for ultraviolet finiteness and confirming known non-renormalisation limits.

Contribution

It introduces a pure spinor formalism approach for supergravity amplitudes, emphasizing manifest supersymmetry and analyzing ultraviolet divergence conditions.

Findings

Amplitude diagrams derived from D=11 supergravity via pure spinor formalism.

Ultraviolet finiteness limits depend on loop order and dimension.

Non-renormalisation fails at 7 loops in four dimensions, aligning with previous results.

Abstract

We present a description for amplitude diagrams in maximal supergravities obtained by dimensional reduction from D=11, derived from a field theory point of view using the pure spinor formalism. The advantages of this approach are the manifest supersymmetry present in the formalism, and the limited number of interaction terms in the action. Furthermore, we investigate the conditions set by this description in order for amplitudes in maximal supergravity to be finite in the ultraviolet limit. Typically, there is an upper limit to the dimension, set by the loop order, which for an arbitrary number of loops is no larger than two. In four dimensions, the non-renormalisation power of the formalism fails for the 7-loop contribution to the 4-point amplitude, all of which is in clear agreement with previous work.