Canonical approach to 2D induced gravity

TL;DR

This paper derives the Liouville theory as a gravitational Wess-Zumino action of the Polyakov string using a canonical approach, linking the form of the action to the Virasoro algebra and quantum effects.

Contribution

It introduces a canonical method to obtain Liouville theory as a gravitational Wess-Zumino action, clarifying the role of the Virasoro algebra and central charge.

Findings

Liouville action arises as a gravitational Wess-Zumino action

The form of the Liouville action is linked to the Virasoro algebra

The coefficient is proportional to the central charge and indicates quantum symmetry breaking

Abstract

Using canonical method the Liouville theory has been obtained as a gravitational Wess-Zumino action of the Polyakov string. From this approach it is clear that the form of the Liouville action is the consequence of the bosonic representation of the Virasoro algebra, and that the coefficient in front of the action is proportional to the central charge and measures the quantum braking of the classical symmetry.