Torsion and geometrostasis in nonlinear sigma models

Abstract

We discuss some general effects produced by adding Wess-Zumino terms to the actions of nonlinear sigma models, an addition which may be made if the underlying field manifold has appropriate homological properties. We emphasize the geometrical aspects of such models, especially the role played by torsion on the field manifold. For general chiral models, we show explicitly that the torsion is simply the structure constant of the underlying Lie group, converted by vielbeine into an antisymmetric rank-three tensor acting on the field manifold. We also investigate in two dimensions the supersymmetric extensions on nonlinear sigma models with torsion, showing how the purely results carry over completely. We consider in some detail the renormalization effects produced by the Wess-Zumino terms using the background field method. In particular, we demonstrate to two-loop order the existence of geometrostasis, i.e. fixed points in the renormalized geometry of the field manifold due to parallelism.