Physical States in Matter-Coupled Dilaton Gravity

TL;DR

This paper explores the quantization of matter-coupled two-dimensional dilaton gravity, revealing a complex spectrum of physical states and discussing methods to address the Virasoro anomaly.

Contribution

It introduces a novel approach to quantizing matter-coupled dilaton gravity, analyzing the effects of different constraint modifications and BRST quantization on the physical state spectrum.

Findings

Zero central charge with specific scalar quantization

Few physical states with modified constraints

Rich spectrum of states with BRST quantization

Abstract

We revisit the quantization of matter-coupled, two-dimensional dilaton gravity. At the classical level and with a cosmological term, a series of field transformations leads to a set of free fields of indefinite signature. Without matter the system is represented by two scalar fields of opposite signature. With a particular quantization for the scalar with negative kinetic energy, the system has zero central charge and we find some physical states satisfying {\it all} the Virasoro conditions. With matter, the constraints cannot be solved because of the Virasoro anomaly. We discuss two avenues for consistent quantization: modification of the constraints, and BRST quantization. The first avenue appears to lead to very few physical states. The second, which roughly corresponds to satisfying half of the Virasoro conditions, results in a rich spectrum of physical states. This spectrum, however, differs significantly from that of free matter fields propagating on flat two-dimensional space-time.