Classical and Quantum Considerations of Two-dimensional Gravity

TL;DR

This paper explores two-dimensional gravity with a graviton-dilaton system, analyzing classical and quantum solutions, and demonstrating anomaly-free quantum behavior regardless of matter conformal dimensions.

Contribution

It introduces a fixed graviton-dilaton coupling that ensures anomaly-free quantum theory across various matter conformal dimensions, including cases without dilaton Lagrange multipliers.

Findings

Quantum theory remains free of conformal anomaly for any matter conformal dimension.

Classical and quantum solutions are derived using canonical quantization.

Interaction terms are incorporated and analyzed within the system.

Abstract

The two-dimensional theory of gravity describing a graviton-dilaton system is considered. The graviton-dilaton coupling can be fixed such that the quantum theory remains free of the conformal anomaly for any conformal dimension of the coupled matter system, even if the dilaton does not appear as Lagrange multiplier. Interaction terms are introduced and the system is analyzed and solutions are given at the classical level and at the quantum level by using canonical quantization.