# Surveying the three-dimensional fixed points of T duality

## Abstract

We explore the family of fixed points of T-duality transformations in three dimensions. For the simplest nontrivial self-duality conditions it is possible to show that, in addition to the spacelike isometry in which the T-duality transformation is performed, these backgrounds must be necessarily stationary. This allows us to prove that, for nontrivial string coupling, the low energy bosonic string backgrounds, which are additionally self-T-dual along an isometry direction generated by a constant norm Killing vector, are uniquely described by a two-parametric class, including only three nonsingular cases: the charged black string, the exact gravitational wave propagating along the extremal black string, and the flat space with a linear dilaton. Besides, for constant string coupling, the only self-T-dual lower energy string background under the same assumptions corresponds to the Coussaert-Henneaux spacetime. Thus, we identify minimum criteria that yield a classification of these quoted examples and only these. All these T-dual fixed points describe exact backgrounds of string theory.

- Authors:

- Centro de Estudios Cientificos (CECS), Casilla 1469, Valdivia (Chile)
- (Mexico)
- Departamento de Fisica, Universidad de Buenos Aires, Ciudad Universitaria, Pabellon I (1428), Buenos Aires (Argentina)

- Publication Date:

- OSTI Identifier:
- 21011123

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. D, Particles Fields; Journal Volume: 75; Journal Issue: 4; Other Information: DOI: 10.1103/PhysRevD.75.046008; (c) 2007 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; COUPLING; DUALITY; GRAVITATIONAL WAVES; QUANTUM FIELD THEORY; SPACE-TIME; STRING MODELS; THREE-DIMENSIONAL CALCULATIONS; TRANSFORMATIONS; VECTORS

### Citation Formats

```
Ayon-Beato, Eloy, Departamento de Fisica, CINVESTAV-IPN, Apdo. Postal 14-740, 07000, Mexico D.F., and Giribet, Gaston.
```*Surveying the three-dimensional fixed points of T duality*. United States: N. p., 2007.
Web. doi:10.1103/PHYSREVD.75.046008.

```
Ayon-Beato, Eloy, Departamento de Fisica, CINVESTAV-IPN, Apdo. Postal 14-740, 07000, Mexico D.F., & Giribet, Gaston.
```*Surveying the three-dimensional fixed points of T duality*. United States. doi:10.1103/PHYSREVD.75.046008.

```
Ayon-Beato, Eloy, Departamento de Fisica, CINVESTAV-IPN, Apdo. Postal 14-740, 07000, Mexico D.F., and Giribet, Gaston. Thu .
"Surveying the three-dimensional fixed points of T duality". United States.
doi:10.1103/PHYSREVD.75.046008.
```

```
@article{osti_21011123,
```

title = {Surveying the three-dimensional fixed points of T duality},

author = {Ayon-Beato, Eloy and Departamento de Fisica, CINVESTAV-IPN, Apdo. Postal 14-740, 07000, Mexico D.F. and Giribet, Gaston},

abstractNote = {We explore the family of fixed points of T-duality transformations in three dimensions. For the simplest nontrivial self-duality conditions it is possible to show that, in addition to the spacelike isometry in which the T-duality transformation is performed, these backgrounds must be necessarily stationary. This allows us to prove that, for nontrivial string coupling, the low energy bosonic string backgrounds, which are additionally self-T-dual along an isometry direction generated by a constant norm Killing vector, are uniquely described by a two-parametric class, including only three nonsingular cases: the charged black string, the exact gravitational wave propagating along the extremal black string, and the flat space with a linear dilaton. Besides, for constant string coupling, the only self-T-dual lower energy string background under the same assumptions corresponds to the Coussaert-Henneaux spacetime. Thus, we identify minimum criteria that yield a classification of these quoted examples and only these. All these T-dual fixed points describe exact backgrounds of string theory.},

doi = {10.1103/PHYSREVD.75.046008},

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

number = 4,

volume = 75,

place = {United States},

year = {Thu Feb 15 00:00:00 EST 2007},

month = {Thu Feb 15 00:00:00 EST 2007}

}