Duality between 1+1 dimensional Maxwell-Dilaton gravity and Liouville field theory

TL;DR

This paper reformulates 2D Maxwell-Dilaton gravity models into a decoupled Liouville field theory with a Maxwell gauge field, providing a new effective action for future quantization studies.

Contribution

It introduces a novel reformulation of 2D dilaton gravity models into a decoupled Liouville field theory with Maxwell field, facilitating analysis and quantization.

Findings

Reformulation into two decoupled Liouville fields in flat space.

Derivation of an effective action capturing dilaton and gravity dynamics.

Potential for canonical quantization of these gravity-matter systems.

Abstract

We present an interesting reformulation of a collection of dilaton gravity models in two space-time dimensions into a field theory of two decoupled Liouville fields in flat space, in the presence of a Maxwell gauge field. An effective action is also obtained, encoding the dynamics of the dilaton field and the single gravitational degree of freedom in a decoupled regime. This effective action represents an interesting starting point for future work, including the canonical quantization of these classes of non trivial models of gravity coupled matter systems.