Anomaly cancellation and one-loop finiteness of 6D half-maximal supergravities

Abstract

We suggest that the surprising one-loop finiteness of 6D half-maximal supergravities recently discovered in \cite{Huang:2025nyr} might be related to anomaly-free $SO(5, 21)$ G-duality symmetry in $(2,0)$ supergravity with 21 tensor multiplets and to anomaly-free $SO(4, 20)$ G-duality symmetry of $(1,1)$ supergravity with 20 vector multiplets. Our argument is reminiscent of the analogous role of the anomaly-free $E_{7(7)}$ G-duality symmetry in the UV finiteness of a maximal 4D supergravity at 3 loops.