Canonical treatment of two dimensional gravity as an anomalous gauge theory

TL;DR

This paper applies the extended phase space method to formulate two-dimensional gravity in various gauges, revealing the connection between BRST symmetry and current algebra, and deriving the conformal gauge action.

Contribution

It introduces a BRST formulation of 2D gravity in different gauges and links gauge symmetry to current algebra structures, providing a unified approach.

Findings

BRST formulation of light-cone gauge established

Relationship between BRST symmetry and $SL(2,R)$ current algebra demonstrated

Derivation of conformal gauge action consistent with previous proposals

Abstract

The extended phase space method of Batalin, Fradkin and Vilkovisky is applied to formulate two dimensional gravity in a general class of gauges. A BRST formulation of the light-cone gauge is presented to reveal the relationship between the BRST symmetry and the origin of $SL(2,R)$ current algebra. From the same principle we derive the conformal gauge action suggested by David, Distler and Kawai.