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

We explain why the surprising one-loop finiteness of 6D half-maximal supergravities recently discovered in \cite{Huang:2025nyr} is the result of the cancellation of the six-dimensional gravitational and gauge anomalies in (2,0) supergravity with 21 tensor multiplets and its anomaly-free SO(5, 21) duality. The one-loop finiteness of (1,1) supergravity with 20 vector multiplets is also explained by anomaly-free SO(4, 20) duality symmetry.

💡 Research Summary

The paper provides a detailed explanation for the surprising one‑loop finiteness recently observed in six‑dimensional half‑maximal supergravity theories. The authors focus on two specific models: (2,0) supergravity coupled to 21 tensor multiplets and (1,1) supergravity coupled to 20 vector multiplets. Both models arise as low‑energy limits of type IIB and type IIA (or heterotic) string compactifications on K3, and they share a common feature: a hidden global duality symmetry G that is an orthogonal group, namely SO(5,21) for the (2,0) theory and SO(4,20) for the (1,1) theory.

The analysis begins by reviewing the field content of the (2,0) theory. The gravitational multiplet contains a self‑dual two‑form, a left‑handed gravitino and five scalars, while each tensor multiplet contributes an anti‑self‑dual two‑form, a right‑handed tensorino and five scalars. The scalars parametrize the coset SO(5,n_T)/