Antibrackets, supersymmetric σ-model and localization

We consider supersymmetrization of Hamiltonian dynamics via antibrackets for systems whose Hamiltonian generates an isometry of the phase space. We find that the models are closely related to the supersymmetric non-linear σ-model. We interpret the corresponding path integrals in terms of super loop space equivariant cohomology. It turns out that they can be evaluated exactly using localizations techniques.