Integrable Models of $(1+1)$-Dimensional Dilaton Gravity Coupled to Scalar Matter

We describe a class of explicitly integrable models of $(1+1)$-dimensional dilaton gravity coupled to scalar fields in sufficient detail. The equations of motion of these models reduce to systems of Liouville equations with energy and momentum constraints. We construct the general solution of the equations and constraints in terms of chiral moduli fields explicitly and briefly discuss some extensions of the basic integrable model. These models can be related to higher-dimensional supergravity theories, but we mostly consider them independently of such interpretations. We also briefly review other integrable models of two-dimensional dilaton gravity.