Modular Classes and Supersymmetric Berezin Volumes

Abstract

We argue that modular classes of \(Q\)-manifolds provide an efficient method for addressing the existence of supersymmetric Berezin volumes in the supergeometric representation theory of the \(\mathcal {N}=2\) \(d=1\) supertranslation algebra. We establish a cohomological coherence criterion for the existence of a Berezin volume that is invariant under both of the supercharges. Abstract Published by the Jagiellonian University 2026 authors