An R4 non-renormalization theorem in super-gravity

Abstract

We consider the four-graviton amplitudes in CHL constructions providing four-dimensional models with various numbers of vector multiplets. We show that in these models the two-loop amplitude has a prefactor of ∂2R4. This implies a non-renormalization theorem for the R4 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 R4 term to the U(1) anomaly of pure super-gravity.