Conformal invariance and string theory in compact space: bosons

Abstract

The area law of the Nambu-Goto string is generalized to include a solid-angle-type term, which is purely topological in nature. Such a term exists and is unique provided the manifold M in which the string lives satisfies certain topological conditions. This generalization may be useful to maintain conformal invariance in case M is compact. Using methods of Polyakov and Friedan we identify the conformal anomaly coefficient with the central charge of the Virasoro algebra of this string theory. As an illustration we choose M to be a compact Lie group and compute the anomaly coefficient following the work of Knizhnik and Zamolodchikov.