53 research outputs found
Surveying the Three-Dimensional Fixed Points of T-Duality
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, additionally to the spacelike isometry in which the T-Duality
transformation is performed, these backgrounds must be necessarily stationary.
This allows 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.Comment: 11 Page
pp Waves of Conformal Gravity with Self-Interacting Source
Recently, Deser, Jackiw and Pi have shown that three-dimensional conformal
gravity with a source given by a conformally coupled scalar field admits pp
wave solutions. In this letter, we consider this model with a self-interacting
potential preserving the conformal structure. A pp wave geometry is also
supported by this system and, we show that this model is equivalent to
topologically massive gravity with a cosmological constant whose value is given
in terms of the potential strength.Comment: 6 pages, minor changes, accepted in Ann. Phy
Uniqueness of the Jackiw non-Noetherian conformal scalar field
Jackiw was undoubtedly the first to exhibit an example of a scalar field
action which is not conformally invariant whereas its equation of motion is.
This feature has recently been dubbed as a non-Noetherian conformal scalar
field. The paradigmatic example of Jackiw was the generalization to curved
spacetime of the two-dimensional Liouville action. Here, we prove that, up to
second order, this is the unique example of a non-Noetherian conformal scalar
field in two dimensions. We establish this result using an old and somewhat
forgotten theorem which is none other than the solution to the inverse problem
of the calculus of variations.Comment: We dedicate this note to Prof. Roman Jackiw, the pioneer in the
exploration of non-Noetherian conformal scalar fields and a champion of
subtle thinking in the wonderland of symmetrie
Scalar Fields Nonminimally Coupled to pp Waves
Here, we report pp waves configurations of three-dimensional gravity for
which a scalar field nonminimally coupled to them acts as a source. In absence
of self-interaction the solutions are gravitational plane waves with a profile
fixed in terms of the scalar wave. In the self-interacting case, only power-law
potentials parameterized by the nonminimal coupling constant are allowed by the
field equations. In contrast with the free case the self-interacting scalar
field does not behave like a wave since it depends only on the wave-front
coordinate. We address the same problem when gravitation is governed by
topologically massive gravity and the source is a free scalar field. From the
pp waves derived in this case, we obtain at the zero topological mass limit,
new pp wave solutions of conformal gravity for any arbitrary value of the
nonminimal coupling parameter. Finally, we extend these solutions to the
self-interacting case of conformal gravity.Comment: 14 pages, RevTeX. Minor changes. To appear in Phys. Rev.
- …