Free differential algebras and generic 2D dilatonic (super)gravities

TL;DR

This paper reformulates 2D dilatonic gravity theories, including supersymmetric versions, as free differential algebras, providing a unified geometric framework and explicit solutions, and explores their relation to traditional formulations and matter coupling.

Contribution

It introduces a free differential algebra approach to generic 2D dilatonic (super)gravity, generalizing gauge formulations and enabling explicit solutions.

Findings

Unified geometric formulation of 2D dilatonic gravity theories.

Explicit general solutions in differential forms.

Analysis of relation to traditional and matter-coupled models.

Abstract

The field equations for both generic bosonic and generic locally supersymmetric 2D dilatonic gravity theories in the absence of matter are written as free differential algebras. This constitutes a generalization of the gauge theoretic formulation. Moreover, it is shown that the condition of free differential algebra can be used to obtain the equations in the locally supersymmetric case. Using this formulation, the general solution of the field equations is found in the language of differential forms. The relation with the ordinary formulation and the coupling to supersymmetric conformal matter are also studied.