Integrable Models of 1+1 Dimensional Dilaton Gravity Coupled to Scalar Matter

TL;DR

This paper presents a class of explicitly integrable 1+1 dimensional dilaton gravity models coupled with scalar fields, providing explicit solutions and discussing their potential connections to higher-dimensional supergravity theories.

Contribution

It introduces a new class of integrable models where equations reduce to Liouville systems, with explicit solutions in terms of chiral moduli fields, expanding the understanding of 2D dilaton gravity.

Findings

Explicit solutions for the models are constructed.

Models reduce to Liouville equations with constraints.

Extensions of the basic integrable models are discussed.

Abstract

A class of explicitly integrable models of 1+1 dimensional dilaton gravity coupled to scalar fields is described in some detail. The equations of motion of these models reduce to systems of the Liouville equations endowed with energy and momentum constraints. The general solution of the equations and constraints in terms of chiral moduli fields is explicitly constructed and some extensions of the basic integrable model are briefly discussed. These models may be related to high dimensional supergravity theories but here they are mostly considered independently of such interpretations. A brief review of other integrable models of two-dimensional dilaton gravity is also given.