Quantum dilaton gravity as a linear dilaton conformal field theory

TL;DR

This paper quantizes a matter-coupled two-dimensional gravity model, achieving anomaly cancellation through parameter tuning, and maps it onto a linear dilaton conformal field theory, revealing its spectrum and matter coupling limits.

Contribution

It introduces a quantization method for matter-coupled 2D gravity that ensures anomaly cancellation and maps the model onto a linear dilaton CFT, extending understanding of its spectrum and matter coupling.

Findings

Pure gauge theory with massless ground state without matter

Ability to couple up to 11 matter scalar fields with a tachyonic ground state

Matter sector decouples similarly to string transverse oscillators

Abstract

A model of matter-coupled gravity in two dimensions is quantized. The crucial requirement for performing the quantization is the vanishing of the conformal anomaly, which is achieved by tuning a parameter in the interaction potential. The spectrum of the theory is determined by mapping the model first onto a field theory with a Liouville interaction, then onto a linear dilaton conformal field theory. In absence of matter fields a pure gauge theory with massless ground state is found; otherwise it is possible to minimally couple up to 11 matter scalar fields: in this case the ground state is tachyonic and the matter sector decouples, like the transverse oscillators in the critical bosonic string.