Counterterms in Supergravity

TL;DR

This paper investigates the ultraviolet divergences in supergravity theories across various dimensions by computing loop amplitudes, revealing non-renormalizability in higher dimensions and suggesting a deep connection between gravity and Yang-Mills theories.

Contribution

It provides the first explicit two-loop amplitude calculations in supergravity and uncovers a relationship between gravity and Yang-Mills amplitudes through a squaring procedure.

Findings

Supergravity is non-renormalizable for D ≥ 6.

Evidence of a five-loop counterterm in D=4 supergravity.

Gravity amplitudes relate to Yang-Mills amplitudes via a squaring relation.

Abstract

We examine the ultraviolet behaviour of supergravity theories as a function of dimension and number of supercharges. We do so by the computation of one and two-loop physical on-shell four point amplitudes. For maximal supergravity, our computations prove the non-renomalisability of supergravity for $D \geq 6$ (including the maximal D=11 case) and give strong evidence for the existance of a five-loop counterterm in D=4. For type I supergravity our results indicate similar patterns. e shall also explore a remarkable relationship between gravity amplitudes and those of Yang-Mills theories. In many ways gravity calculations discover features which relate to the equivalent Yang-Mills features by a squaring proceedure.