Antibrackets, Supersymmetric $\sigma$-Model and Localization

TL;DR

This paper explores the supersymmetrization of Hamiltonian dynamics using antibrackets, relating it to supersymmetric sigma-models and demonstrating exact evaluation via localization in super loop space cohomology.

Contribution

It introduces a novel supersymmetrization approach for Hamiltonian systems with isometries, connecting it to supersymmetric sigma-models and applying localization techniques for exact results.

Findings

Models are closely related to supersymmetric non-linear sigma-models.

Path integrals can be evaluated exactly using localization.

Super loop space equivariant cohomology provides a framework for analysis.

Abstract

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 $\sigma$-model. We interpret the corres\-ponding path integrals in terms of super loop space equivariant cohomology. It turns out that they can be evaluated exactly using localizations techniques.