DOUBLE SCALING LIMITS AND AIRY FUNCTIONS FROM QUASIHOMOGENEOUS SINGULARITIES OF VECTOR SIGMA MODELS

A sufficiently large class of vector sigma models admitting r variable singularities is defined. It is shown how quasihomogeneity induces filtrations on algebras of functions and Lie algebras of infinitesimal diffeomorphisms. From the filtrations, double scaling limits and Airy functions are derived.