Background charges and consistent continuous deformations of $2d$ gravity theories

TL;DR

This paper classifies background charges and continuous deformations of 2D gravity theories with scalar matter, revealing conditions for their existence and proposing new models potentially related to non-critical string theories.

Contribution

It systematically constructs all background charges and deformations of 2D gravity with scalar matter, linking their existence to special Killing vectors in the target space.

Findings

Deformations exist only if the target space has a covariantly constant null Killing vector.

Deformed actions lead to novel 2D gravity models.

Some models may correspond to non-critical string theories.

Abstract

We construct and discuss all background charges and continuous consistent deformations of standard $2d$ gravity theories with scalar matter fields. It turns out that the background charges and those deformations which change nontrivially both the form of the action and of its gauge symmetries are closely linked and exist only if the target space has at least one special (`covariantly constant') Killing vector which must be a null vector in the case of the deformations. The deformed actions provide interesting novel $2d$ gravity models. We argue that some of them lead to non-critical string theories.