# Killing vector fields and harmonic superfield theories

## Abstract

The harmonic action functional allows a natural generalisation to semi-Riemannian supergeometry, also referred to as harmonic, which resembles the supersymmetric sigma models studied in high energy physics. We show that Killing vector fields are infinitesimal supersymmetries of this harmonic 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.

- Authors:

- Humboldt-Universität zu Berlin, Institut für Mathematik, Rudower Chaussee 25, 12489 Berlin (Germany)

- Publication Date:

- OSTI Identifier:
- 22306042

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Mathematical Physics

- Additional Journal Information:
- Journal Volume: 55; Journal Issue: 9; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0022-2488

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; HIGH ENERGY PHYSICS; MATHEMATICAL MODELS; RIEMANN SPACE; SIGMA MODEL; SUPERSYMMETRY; VECTOR FIELDS

### Citation Formats

```
Groeger, Josua, E-mail: groegerj@mathematik.hu-berlin.de.
```*Killing vector fields and harmonic superfield theories*. United States: N. p., 2014.
Web. doi:10.1063/1.4895464.

```
Groeger, Josua, E-mail: groegerj@mathematik.hu-berlin.de.
```*Killing vector fields and harmonic superfield theories*. United States. doi:10.1063/1.4895464.

```
Groeger, Josua, E-mail: groegerj@mathematik.hu-berlin.de. Mon .
"Killing vector fields and harmonic superfield theories". United States. doi:10.1063/1.4895464.
```

```
@article{osti_22306042,
```

title = {Killing vector fields and harmonic superfield theories},

author = {Groeger, Josua, E-mail: groegerj@mathematik.hu-berlin.de},

abstractNote = {The harmonic action functional allows a natural generalisation to semi-Riemannian supergeometry, also referred to as harmonic, which resembles the supersymmetric sigma models studied in high energy physics. We show that Killing vector fields are infinitesimal supersymmetries of this harmonic 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.},

doi = {10.1063/1.4895464},

journal = {Journal of Mathematical Physics},

issn = {0022-2488},

number = 9,

volume = 55,

place = {United States},

year = {2014},

month = {9}

}

DOI: 10.1063/1.4895464

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