Coset Models and Differential Geometry

TL;DR

This paper explores how string propagation in curved backgrounds relates to differential geometry, showing that classical string dynamics often involve two-dimensional sigma-models linked to coset conformal field theories.

Contribution

It demonstrates that in many curved backgrounds, the classical string dynamics can be described by 2D sigma-models associated with coset conformal field theories, connecting string theory and differential geometry.

Findings

Classical string dynamics involve 2D sigma-models.

These models correspond to coset conformal field theories.

The approach links string propagation to differential geometric embedding problems.

Abstract

String propagation on a curved background defines an embedding problem of surfaces in differential geometry. Using this, we show that in a wide class of backgrounds the classical dynamics of the physical degrees of freedom of the string involves 2-dim sigma-models corresponding to coset conformal field theories.