Quantization of a Theory of 2d Dilaton Gravity

TL;DR

This paper investigates the quantization of the 2D CGHS dilaton gravity model, revealing that the quantum behavior varies significantly depending on the number of matter fields, affecting the presence of singularities and the semi-classical limits.

Contribution

It provides a detailed analysis of the quantum properties of the 2D CGHS model, highlighting the dependence on matter field count and contrasting different regimes.

Findings

Singularity absence when matter fields are fewer than 24

Different quantum regimes for matter fields above and below 24

Quantum theory aligns with semi-classical limits in specific regimes

Abstract

We discuss the quantization of the 2d gravity theory of Callan, Giddings, Harvey, and Strominger (CGHS), following the procedure of David, and of Distler and Kawai. We find that the physics depends crucially on whether the number of matter fields is greater than or less than 24. In the latter case the singularity pointed out by several authors is absent but the physical interpretation is unclear. In the former case (the one studied by CGHS) the quantum theory which gives CGHS in the linear dilaton semi-classical limit, is different from that which gives CGHS in the extreme Liouville regime.