Killing Vector Fields and Superharmonic Field Theories

TL;DR

This paper explores the role of Killing vector fields as symmetries in superharmonic field theories within semi-Riemannian supergeometry, establishing Noether theorems and characterizations of these vector fields.

Contribution

It introduces a unified approach to characterizing Killing vector fields in semi-Riemannian supermanifolds and demonstrates their significance as infinitesimal supersymmetries in superharmonic actions.

Findings

Killing vector fields are infinitesimal supersymmetries of superharmonic action.

Proves three different Noether theorems in this context.

Provides a comprehensive treatment of characterizations of Killing vector fields.

Abstract

The harmonic action functional allows a natural generalisation to semi-Riemannian supergeometry, referred to as superharmonic action, which resembles the supersymmetric sigma models studied in high energy physics. We show that Killing vector fields are infinitesimal supersymmetries of the superharmonic action and prove three different Noether theorems in this context. En passant, we provide a homogeneous treatment of five characterisations of Killing vector fields on semi-Riemannian supermanifolds, thus filling a gap in the literature.