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

TL;DR

The paper explores the potential link between one-loop finiteness in 6D half-maximal supergravities and anomaly-free G-duality symmetries, drawing parallels with known symmetries in other supergravity theories.

Contribution

It proposes a connection between anomaly cancellation and one-loop finiteness in 6D supergravities, inspired by symmetry considerations.

Findings

One-loop finiteness may be related to anomaly-free G-duality symmetries.

The argument draws parallels with the role of $E_{7(7)}$ symmetry in 4D supergravity.

The paper suggests a symmetry-based explanation for finiteness in specific supergravity models.

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.