A U(1) Current Algebra Model Coupled to 2D-Gravity

TL;DR

This paper explores a scalar field model with U(1) current algebra coupled to 2D gravity, revealing symmetry structures, central extensions, and connections to advanced gravity theories.

Contribution

It introduces a simple U(1) current algebra model coupled to 2D gravity, analyzing its symmetries, central extensions, and relation to W-infinity gravity.

Findings

Identified the possible central extension of the symmetry algebra.

Determined the critical dimension of the model.

Showed the interdependence of symmetry generators.

Abstract

We consider a simple model of a scalar field with $U(1)$ current algebra gauge symmetry coupled to $2D$-gravity in order to clarify the origin of Stuckelberg symmetry in the $w_{\infty}$-gravity theory. An analogous symmetry takes place in our model too. The possible central extension of the complete symmetry algebra and the corresponding critical dimension have been found. The analysis of the Hamiltonian and the constraints shows that the generators of the current algebra, the reparametrization and the Stuckelberg symmetries are not independent. The connection of the model with $w_{1+\infty}-$ and $W_{1+\infty}$-gravity is discussed.