Universal aspects of string propagation on curved backgrounds

TL;DR

This paper explores the universal geometric and algebraic structures underlying string propagation on curved backgrounds, linking conformal field theory, embedding surfaces, and parafermions.

Contribution

It demonstrates the universality of the classical dynamics of strings on certain curved backgrounds and introduces parafermions into the geometric framework.

Findings

Classical string dynamics are governed by a universal coset conformal field theory.

String propagation on flat and curved backgrounds shares common geometric features.

Parafermions are essential in integrating the Gauss-Codazzi equations in this context.

Abstract

String propagation on D-dimensional curved backgrounds with Lorentzian signature is formulated as a geometrical problem of embedding surfaces. When the spatial part of the background corresponds to a general WZW model for a compact group, the classical dynamics of the physical degrees of freedom is governed by the coset conformal field theory SO(D-1)/SO(D-2), which is universal irrespective of the particular WZW model. The same holds for string propagation on D-dimensional flat space. The integration of the corresponding Gauss-Codazzi equations requires the introduction of (non-Abelian) parafermions in differential geometry.