On Poisson geometry and supersymmetric sigma models

TL;DR

This paper introduces a Poisson geometric framework for supersymmetric field theories, enabling invariant calculations and the construction of supersymmetric sigma models on the supersphere.

Contribution

It develops a novel formalism using Poisson geometry for handling $UOSp(2|1)$-supersymmetric theories with superfields and applies it to construct the Kalb-Ramond term.

Findings

A new invariant formalism for supersymmetric theories using Poisson brackets.

Explicit construction of the Kalb-Ramond term on the supersphere.

Simplified calculations in supersymmetric sigma models.

Abstract

By using the Poisson geometry, we develop a manifestly invariant and calculation-friendly formalism for handling $UOSp(2|1)$-supersymmetric field theories. In particular, the super-Langrangians are written solely in terms of superfields, Poisson brackets and the moment map generating the $UOSp(2|1)$ action. As an application of this formalism, we construct the Kalb-Ramond term for supersymmetric sigma models on the supersphere.