2D induced gravity from canonically gauged WZNW system

TL;DR

This paper constructs a 2D induced gravity model from a gauge-invariant extension of the WZNW system based on SL(2,R), demonstrating its geometric properties through canonical and Dirac bracket formalisms.

Contribution

It introduces a gauge theory formulation of 2D induced gravity derived from a canonical gauging of the WZNW model, linking gauge invariance to gravitational dynamics.

Findings

Effective theory matches 2D induced gravity after gauge fixing.

Geometric properties derived from gauge invariance and Dirac brackets.

Framework connects WZNW models to gravitational theories.

Abstract

Starting from the Kac--Moody structure of the WZNW model for SL(2,R) and using the general canonical formalism, we formulate a gauge theory invariant under local SL(2,R) x SL(2,R) and diffeomorphisms. This theory represents a gauge extension of the WZNW system, defined by a difference of two simple WZNW actions. By performing a partial gauge fixing and integrating out some dynamical variables, we prove that the resulting effective theory coincides with the induced gravity in 2D. The geometric properties of the induced gravity are obtained out of the gauge properties of the WZNW system with the help of the Dirac bracket formalism.