Surprising One-Loop Finiteness of 6D Half-Maximal Supergravities

In four dimensions, it has long been established that gravity coupled to matter exhibits ultraviolet divergences at one loop, irrespective of supersymmetry. Notably, the four-matter one-loop amplitudes of half-maximal supergravity coupled to Maxwell multiplets were shown in the 1970s to be divergent. Surprisingly, we demonstrate in this Letter that half-maximal theories can nevertheless become one-loop finite when uplifted to higher dimensions, contrary to naive expectations. Specifically, we study the ultraviolet properties of the four-matter and two-matter two-graviton amplitudes in six-dimensional N=(2,0) and N=(1,1) supergravities, coupled to n_{T} tensor and n_{V} vector multiplets, respectively. We find that the one-loop amplitudes are finite for n_{T}=21 and n_{V}=20. This finiteness is unexpected, as symmetry-preserving counterterms do exist. Interestingly, both values exactly correspond to low-energy limits of type II string theories compactified on K3, which hints at possible origins to the surprising cancellations.