The Topology of Area-Preserving Diffeomorphism Groups and Large N Limits of Classical Groups

By John Swain, Northeastern University

It is by now common practice to regard the large N limits of classical groups, especially SU(N) for N large, as being connected in some way with groups of area-preserving diffeomorphisms of 2-dimensional manifolds. Treatments at the Lie algebra level using infinitesimal transformations require delicate handling of the limiting procedures used. This paper shows that while infinitesimal considerations are suggestive of a connection, the large classical groups provide very poor approximations to the global topology of area preserving diffeomorphism groups. Some comments are made with respect to what this might mean for membrane and string theories.