A new look at the RST model

TL;DR

This paper revisits the RST model by adding a scalar field and boundary term, revealing a hidden dynamical field that ensures local invariance, proper constraint algebra, and explains the model's parameter structure.

Contribution

It introduces a boundary term and scalar field to the RST model, enabling a complete constraint analysis and uncovering a hidden dynamical field that clarifies its invariance and parameter differences.

Findings

The augmented RST model is well-posed and local.

A hidden dynamical field in the RST model is identified.

The constraint algebra is reconstructed, ensuring invariance.

Abstract

The RST model is augmented by the addition of a scalar field and a boundary term so that it is well-posed and local. Expressing the RST action in terms of the ADM formulation, the constraint structure can be analysed completely. It is shown that from the view point of local field theories, there exists a hidden dynamical field in the RST model. Thanks to the presence of this hidden dynamical field, we can reconstruct the closed algebra of the constraints which guarantee the general invariance of the RST action. The resulting stress tensors are recovered to be true tensor quantities. At the quantum level, the cancellation condition for the total central charge is reexamined. Finally, with the help of the hidden dynamical field, the fact that the semi-classical static solution of the RST model has two independent parameters (P,M), whereas for the classical CGHS model there is only one, can be explained.