Conformal and non-conformal symmetries in 2D dilaton gravity

Abstract

We study finite-dimensional extra symmetries of generic 2D dilaton gravity models. Using a non-linear sigma model formulation we show that the unique theories admitting an extra (conformal) symmetry are the models with an ex-which include the model of Callan, Giddings, Harvey and Strominger (CGHS) as a particular though limiting (β = 0) case. These models give rise to black hole solutions with * Work partially supported by the Comisión Interministerial de Ciencia y Tecnología and DGICYT. † cruz@lie.uv.es ‡ jnavarro@lie.uv.es § mnavarro@ugr.es ¶ talavera@lie.uv.es a mass-dependent temperature. The underlying extra symmetry can be maintained in a natural way in the one-loop effective action, thus implying the exact solubility of the semiclassical theory including back-reaction. Moreover, we also introduce three different classes of (non-conformal) transformations which are extra symmetries for generic 2D dilaton gravity models. Special linear combinations of these transformations turn out to be the (conformal) symmetries of the CGHS and V ∝ e βφ models. We show that one of the non-conformal extra symmetries can be converted into a conformal one by means of adequate field redefinitions involving the metric and the derivatives of the dilaton. Finally, by expressing the Polyakov-Liouville effective action in terms of an invariant metric, we are able to provide semiclassical models which are also invariant. This generalizes the solvable semiclassical model of Bose, Parker and Peleg (BPP)for a generic 2D dilaton gravity model.

(Generalized) conformal quantum mechanics of 0-branes and two-dimensional dilaton gravity

“…We shall come back to this point later in this section. In general, with an arbitrary potential V (φ) the two-dimensional dilaton gravity model with the action (26) has the symmetry under the following transformations [26]:…”

Non-perturbative path integral of 2d dilaton gravity and two-loop effects from scalar matter

“…These theories still contain a vast variety of models allowing de facto an arbitrary topological structure which may be designed at will following a simple set of rules [22,24]. Recently a particular example of a black hole solution determined by V (X) ∝ exp(X) has been advocated by Cruz et al [25] which reflects the same classical features as the CGHS model [14].…”

“…There are only two exceptions: Either a polynomial behaviour of V , where only a finite number of coefficients need to be redefined, or an exponential behaviour V (X) = α exp(βX) where the renormalized potential is an exponential again and only one parameter α needs to be renormalized. Note that this potential gives black hole solutions [25], sharing however with the dilaton black hole of [14] the null-completeness at the singularity [6].…”

Black hole evaporation by thermal bath removal

“…It was shown in Ref [8] that the unique theories admitting special conformal symmetries are the models with a classical exponential potential…”

“…The black hole mass can be calculated immediately [8]: M = 2 βπ |C|. Therefore, the Hawking temperature turns out to be proportional to the mass: T = β 4 M .…”