# On conservation laws for the supersymmetric sigma model

## TL;DR

This paper derives conservation laws for Dirac-harmonic maps, especially on spherical manifolds, and explores their geometric and analytic applications.

## Contribution

It introduces new conservation laws for Dirac-harmonic maps on manifolds with isometries, focusing on the spherical case, and discusses their applications.

## Key findings

- Conservation laws are established for Dirac-harmonic maps.
- Applications to geometric analysis are demonstrated.
- Focus on spherical manifolds enhances understanding of symmetries.

## Abstract

We derive conservation laws for Dirac-harmonic maps and their extensions to manifolds that have isometries, where we mostly focus on the spherical case. In addition, we discuss several geometric and analytic applications of the latter.