Symmetries of 2-d Gravity

TL;DR

This paper explains the origin of the sl(2,R) current algebra in 2D gravity, showing it arises from the topological field theory structure with an sl(2,R) gauge group.

Contribution

It reveals that the sl(2,R) current algebra in 2D gravity originates from the topological gauge group structure, providing a new understanding of its fundamental symmetry.

Findings

2D gravity exhibits an sl(2,R) current algebra

The algebra stems from the topological gauge group structure

Provides insight into the symmetry origin in 2D gravity

Abstract

Two-dimensional gravity in the light-cone gauge was shown to exhibit an underlying sl(2,R) current algebra. It is the purpose of this note to offer a possible explanation about the origin of this important algebra. The essential point is that two-dimensional gravity is governed by a topological field theory. The gauge group is sl(2,R) and it is this enhanced gauge group that yields Polyakov's current algebra.