Weyl transformation and regular solutions in a deformed Jackiw-Teitelboim model

TL;DR

This paper uses a Weyl transformation to find regular solutions in a deformed Jackiw-Teitelboim model with a Liouville-type potential, enabling the construction of non-pathological black hole solutions with computable entropy.

Contribution

It introduces a Weyl transformation approach to obtain regular solutions in a deformed JT model with a Liouville potential, overcoming previous singularities.

Findings

Regular solutions constructed with conformal matter coupling.

Black hole entropy matches boundary stress tensor calculations.

Weyl transformation yields non-pathological models with well-defined thermodynamics.

Abstract

We revisit a deformed Jackiw-Teitelboim model with a hyperbolic dilaton potential, constructed in the preceding work [arXiv:1701.06340]. Several solutions are discussed in a series of the subsequent papers, but all of them are pathological because of a naked singularity intrinsic to the deformation. In this paper, by employing a Weyl transformation to the original deformed model, we consider a Liouville-type potential with a cosmological constant term. Then regular solutions can be constructed with coupling to a conformal matter by using $SL(2)$ transformations. For a black hole solution, the Bekenstein-Hawking entropy is computed from the area law. It can also be reproduced by evaluating the boundary stress tensor with an appropriate local counter-term (which is essentially provided by a Liouville-type potential).