# Null structure groups in eleven dimensions

## Abstract

We classify all the structure groups which arise as subgroups of the isotropy group (Spin(7)xR{sup 8})xR, of a single null Killing spinor in 11 dimensions. We construct the spaces of spinors fixed by these groups. We determine the conditions under which structure subgroups of the maximal null structure group (Spin(7)xR{sup 8})xR may also be embedded in SU(5), and hence the conditions under which a supersymmetric spacetime admits only null, or both timelike and null, Killing spinors. We discuss how this purely algebraic material will facilitate the direct analysis of the Killing spinor equation of 11 dimensional supergravity, and the classification of supersymmetric spacetimes therein.

- Authors:

- DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA (United Kingdom)

- Publication Date:

- OSTI Identifier:
- 20776783

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. D, Particles Fields; Journal Volume: 73; Journal Issue: 4; Other Information: DOI: 10.1103/PhysRevD.73.045011; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; ISOTROPY; MANY-DIMENSIONAL CALCULATIONS; QUANTUM FIELD THEORY; SPACE; SPACE-TIME; SPIN; SPINORS; SU-5 GROUPS; SUPERGRAVITY; SUPERSYMMETRY

### Citation Formats

```
Cariglia, Marco, and Mac Conamhna, Oisin A. P.
```*Null structure groups in eleven dimensions*. United States: N. p., 2006.
Web. doi:10.1103/PhysRevD.73.045011.

```
Cariglia, Marco, & Mac Conamhna, Oisin A. P.
```*Null structure groups in eleven dimensions*. United States. doi:10.1103/PhysRevD.73.045011.

```
Cariglia, Marco, and Mac Conamhna, Oisin A. P. Wed .
"Null structure groups in eleven dimensions". United States.
doi:10.1103/PhysRevD.73.045011.
```

```
@article{osti_20776783,
```

title = {Null structure groups in eleven dimensions},

author = {Cariglia, Marco and Mac Conamhna, Oisin A. P.},

abstractNote = {We classify all the structure groups which arise as subgroups of the isotropy group (Spin(7)xR{sup 8})xR, of a single null Killing spinor in 11 dimensions. We construct the spaces of spinors fixed by these groups. We determine the conditions under which structure subgroups of the maximal null structure group (Spin(7)xR{sup 8})xR may also be embedded in SU(5), and hence the conditions under which a supersymmetric spacetime admits only null, or both timelike and null, Killing spinors. We discuss how this purely algebraic material will facilitate the direct analysis of the Killing spinor equation of 11 dimensional supergravity, and the classification of supersymmetric spacetimes therein.},

doi = {10.1103/PhysRevD.73.045011},

journal = {Physical Review. D, Particles Fields},

number = 4,

volume = 73,

place = {United States},

year = {Wed Feb 15 00:00:00 EST 2006},

month = {Wed Feb 15 00:00:00 EST 2006}

}

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