Gravitational anomalies from the action for self-dual antisymmetric tensor fields in 4k+2 dimensions

Abstract
We show that recent actions for a single self-dual antisymmetric tensor field in 4k+2 dimensions lead to the same one-loop gravitational anomalies as obtained a few years ago by Alvarez-Gaumé and Witten, who conjectured the necessary Feynman rules in the absence of an action principle.