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

TL;DR

This work addresses the ultraviolet behavior of four-dimensional N=4 supergravity by computing one- and two-loop four-graviton amplitudes in CHL heterotic string models and taking the field-theory limit. It finds that the one-loop contribution factorizes the $t_8t_8R^4$ structure, while the two-loop contribution yields a $∂^2R^4$ factor, implying a non-renormalisation of the $R^4$ term beyond one loop and ruling out a three-loop divergence in 4D. The analysis hinges on the preservation of the left-moving sector in CHL constructions, fermionic zero-mode saturation, and connections to the U(1) anomaly, with implications that extend across CHL models with varying numbers of vector multiplets. While supporting an overall UV finiteness for the four-graviton amplitude at three loops in pure N=4 supergravity, the paper also discusses caveats from fully supersymmetric $R^4$ counterterms and the nuanced role of anomaly-driven protection.

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.

Figures (1)

• Figure 1: Parametrisation of the two-loop diagram in field theory. Figure (a) is the vacuum diagram and the definition of the proper times, and figures (b) and (c) the two configurations contributing to the four-point amplitude.