Grassmannian Sigma Models

Abstract

We show that sigma models with orthogonal and symplectic Grassmannian target spaces admit chiral Gross-Neveu model formulations, thus extending earlier results on unitary Grassmannians. As a first application, we calculate the one-loop $\beta$-functions in this formalism, showing that they are proportional to the dual Coxeter numbers of the respective symmetry algebras.

51 pages, 7 figures