# Symmetries and conservation laws of a nonlinear sigma model with gravitino

## TL;DR

This paper investigates the symmetries and conservation laws of a nonlinear sigma model with gravitino, revealing invariance under various transformations and providing geometric interpretations of key physical quantities.

## Contribution

It demonstrates invariance of the model's action under conformal, super Weyl transformations, and diffeomorphisms, and offers a geometric explanation of how metric variations affect spinors.

## Key findings

- Invariance under rescaled conformal transformations, super Weyl transformations, and diffeomorphisms.
- Degenerate super symmetry present despite commutative variables.
- Energy-momentum tensor and supercurrent as holomorphic sections.

## Abstract

We show that the action functional of the nonlinear sigma model with gravitino considered in a previous article [18] is invariant under rescaled conformal transformations, super Weyl transformations and diffeomorphisms. We give a careful geometric explanation how a variation of the metric leads to the corresponding variation of the spinors. In particular cases and despite using only commutative variables, the functional possesses a degenerate super symmetry. The corresponding conservation laws lead to a geometric interpretation of the energy-momentum tensor and supercurrent as holomorphic sections of appropriate bundles.