Two-dimensional Liouville Gravity Theory with Non-Trivial Classical Background

TL;DR

This paper explores incorporating a non-trivial classical background into 2D Liouville gravity, revealing that the target space dimension D can exceed 1 by analyzing conformal dimensions of the metric's Weyl factor.

Contribution

It introduces a method to include a classical background metric in 2D Liouville gravity and demonstrates that this allows for target space dimensions greater than one.

Findings

Classical background can be integrated into 2D Liouville gravity.

Target space dimension D can be greater than 1.

The conformal dimensions of background and quantum sectors sum to (1,1).

Abstract

We examine a possibility to introduce a non-trivial classical background metric into the 2-d Liouville gravity theory. The classical background appears as a part of the Weyl factor of the physical metric of 2-d surfaces with some conformal dimension. On the other hand, the rest part of the factor corresponds to the quantum fluctuating sector, having another conformal dimension such that these two conformal dimensions sum up to just (1,1). Consequently we conclude that, in the 2-d Liouville gravity, the target space dimensions D can be beyond 1.