Surprising one-loop finiteness of 6D half-maximal supergravities

TL;DR

This paper reveals that certain six-dimensional half-maximal supergravity theories exhibit unexpected one-loop finiteness, linked to string theory compactifications, challenging previous expectations about divergences.

Contribution

It demonstrates that 6D half-maximal supergravities can be one-loop finite for specific matter multiplet counts, contrary to naive expectations and previous four-dimensional results.

Findings

One-loop amplitudes are finite for n_T=21 and n_V=20.

Finiteness occurs despite the existence of symmetry-preserving counterterms.

Values correspond to low-energy limits of type II string theories on K3.

Abstract

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 work 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 $\mathcal{N}=(2,0)$ and $\mathcal{N}=(1,1)$ 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.