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

Understand

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.