Scalar-Tensor Quantum Gravity in Two Dimensions

TL;DR

This paper explores classical and quantum aspects of two-dimensional scalar-tensor gravity models, demonstrating renormalizability and finiteness in specific cases, and discusses the effective action considering quantum anomalies.

Contribution

It introduces a general class of 2D gravity models with scalar fields, showing their renormalizability and finiteness, and proposes effective actions incorporating quantum anomalies.

Findings

Liouville-type models are renormalisable at the quantum level.

A specific model with black hole solutions is finite.

The effective action includes quantum anomaly terms.

Abstract

We discuss some classical and quantum properties of 2d gravity models involving metric and a scalar field. Different models are parametrized in terms of a scalar potential. We show that a general Liouville-type model with exponential potential and linear curvature coupling is renormalisable at the quantum level while a particular model (corresponding to D=2 graviton-dilaton string effective action and having a black hole solution) is finite. We use the condition of a ``split" Weyl symmetry to suggest possible expressions for the ``effective" action which includes the quantum anomaly term.