The Batalin-Vilkovisky formalism of the spinning particle

TL;DR

This paper demonstrates that the spinning particle model in a flat background coupled to D=1 supergravity violates Felder and Kazhdan's axiom by exhibiting nontrivial cohomology in all negative degrees, challenging existing assumptions in BV formalism.

Contribution

It provides a counterexample showing the Felder-Kazhdan axiom does not hold universally in the BV formalism for certain supersymmetric models.

Findings

Nontrivial negative degree cohomology in the spinning particle model

Violation of Felder-Kazhdan axiom in this context

Cohomology persists regardless of spacetime dimension

Abstract

We show that the axiom of Felder and Kazhdan on the vanishing of the cohomology groups in negative degree associated to solutions of the classical master equation in the Batalin-Vilkovisky formalism is violated by the spinning particle in a flat background coupled to D=1 supergravity. In this model, there are nontrivial cohomology groups in all negative degrees, regardless of the dimension of the spacetime in which the spinning particle is propagating.