Conformal field theory of a space-filling string of gravitational ancestry

TL;DR

This paper develops a classical conformal field theory for a space-filling string in two-dimensional spacetime, exploring its symmetries, invariances, and relation to two-dimensional gravity, without addressing quantum aspects.

Contribution

It introduces a classical conformal field theory for a space-filling string, linking deformations to conformal transformations and analyzing the associated algebra and invariances.

Findings

Realization of conformal algebra with a classical central charge

Analysis of the action's conformal and Weyl invariances

Study of energy-momentum tensor and anomaly cancellation

Abstract

We present a classical conformal field theory on an arbitrary two-dimensional spacetime background. The dynamical object is a space-filling string, and the evolution may be thought as occurring on the manifold of the conformal group. The theory is a "descendant" of the theory of gravitation in two-dimensional spacetime. The discussion is based on the relation of the deformations of the space-filling string with conformal transformations. The realization of the conformal algebra in terms of surface deformations possesses a classical central charge. The action principle, the conformal and Weyl invariances of the action, and the equations of motion are studied. The energy-momentum tensor, the coupling to Liouville matter, and the cancellation of anomalies are analyzed. The quantum theory is not discussed.