Two-Dilaton Theories in Two Dimensions from Dimensional Reduction

TL;DR

This paper classifies two-dimensional gravity theories with two dilatons, showing that most models fall into two main classes, and constructs a first order formulation leading to conservation laws.

Contribution

It provides a comprehensive classification of two-dilaton gravity theories in two dimensions and develops a first order formulation for these classes.

Findings

Most models are either factorizable simple or factorizable conformally simple theories.

A first order formulation is constructed for these classes.

An absolute conservation law is established for the theories.

Abstract

Dimensional reduction of generalized gravity theories or string theories generically yields dilaton fields in the lower-dimensional effective theory. Thus at the level of D=4 theories, and cosmology many models contain more than just one scalar field (e.g. inflaton, Higgs, quintessence). Our present work is restricted to two-dimensional gravity theories with only two dilatons which nevertheless allow a large class of physical applications. The notions of factorizability, simplicity and conformal simplicity, Einstein form and Jordan form are the basis of an adequate classification. We show that practically all physically motivated models belong either to the class of factorizable simple theories (e.g. dimensionally reduced gravity, bosonic string) or to factorizable conformally simple theories (e.g. spherically reduced Scalar-Tensor theories). For these theories a first order formulation is constructed straightforwardly. As a consequence an absolute conservation law can be established.