Real grassmannian ?-models and the extrinsic geometry of strings

Abstract

We discuss the interplay between the extrinsic geometry of strings and the symmetric KahlerianG2,n σ-model coupled with two-dimensional gravity. It is shown that the recently proposed Polyakov's action classically corresponds to a particular topological sector of theG2,n model. The geometrical and physical meaning of the other topological sectors are also examined and shown to be related to the geometry of line bundles over Riemann surfaces (e.g. spinor bundles). The one-loop quantization of the model, around istanton-like solutions, provides scaling behaviour and asymptotic freedom for the adimensional coupling.