An R^4 non-renormalisation theorem in N=4 supergravity

TL;DR

This paper proves a non-renormalisation theorem for the R^4 term in four-dimensional N=4 supergravity, showing it is protected from three-loop ultraviolet divergences due to a specific amplitude structure and its relation to the U(1) anomaly.

Contribution

It establishes an R^4 non-renormalisation theorem in N=4 supergravity, linking amplitude structure to anomaly considerations and constraining ultraviolet divergences.

Findings

Two-loop four-graviton amplitude has a d^2R^4 prefactor.

The R^4 term is protected from three-loop divergences.

Connection between R^4 non-renormalisation and the U(1) anomaly.

Abstract

We consider the four-graviton amplitudes in CHL constructions providing four-dimensional N=4 models with various numbers of vector multiplets. We show that in these models the two-loop amplitude has a prefactor of d^2R^4. This implies a non-renormalisation theorem for the R^4 term, which forbids the appearance of a three-loop ultraviolet divergence in four dimensions in the four-graviton amplitude. We connect the special nature of the R^4 term to the U(1) anomaly of pure N=4 supergravity.