Quantum Theories of Dilaton Gravity

TL;DR

This paper explores the quantization of two-dimensional dilaton gravity coupled with conformal matter, analyzing the theory's conformal invariance, renormalization, and physical viability of different initial data choices.

Contribution

It establishes a connection between background metric independence and conformal invariance in the sigma model formulation of dilaton gravity, and discusses constraints for physically sensible quantum theories.

Findings

The theory is renormalizable but requires new coupling constants at each perturbation order.

Certain initial data lead to unphysical theories with unbounded energies.

Potential modifications to avoid unphysical solutions are briefly considered.

Abstract

Quantization of two-dimensional dilaton gravity coupled to conformal matter is investigated. Working in conformal gauge about a fixed background metric, the theory may be viewed as a sigma model whose target space is parameterized by the dilaton $\phi$ and conformal factor $\rho$. A precise connection is given between the constraint that the theory be independent of the background metric and conformal invariance of the resulting sigma model. Although the action is renormalizable, new coupling constants must be specified at each order in perturbation theory in order to determine the quantum theory. These constants may be viewed as initial data for the beta function equations. It is argued that not all choices of this data correspond to physically sensible theories of gravity, and physically motivated constraints on the data are discussed. In particular a recently constructed subclass of initial data which reduces the full quantum theory to a soluble Liouville-like theory has energies unbounded from below and thus is unphysical. Possibilities for modifying this construction so as to avoid this difficulty are briefly discussed.