On the Equivalence between 2D Induced Gravity and a WZNW system

TL;DR

This paper demonstrates that two-dimensional induced gravity can be equivalently described by a WZNW system based on SL(2,R), linking gauge invariance to Kac-Moody algebra structures.

Contribution

It introduces a general method to construct gauge invariant actions and proves the equivalence between 2D induced gravity and a specific WZNW model.

Findings

Establishes the equivalence between 2D induced gravity and a WZNW system.

Shows that diffeomorphism invariance arises from SL(2,R) Kac-Moody symmetry.

Provides a framework for relating gravity theories to WZNW models.

Abstract

A general method of constructing canonical gauge invariant actions is used to establish the equivalence between 2D induced gravity and a WZNW system, defined by a difference of two simple WZNW actions fo the SL(2,R) group. The diffeomorphism invariance of the induced gravity is generated by the SL(2,R) Kac-Moody structure of the WZNW system.