A GAUGED NONLINEAR SIGMA-MODEL REALIZATION OF THE SYMPLECTIC BLOWING-UP

In this paper a two dimensional non-linear sigma model with a general symplectic manifold with isometry as target space is used to study sym plectic blowing up of a point singularity on the zero level set of the moment map associated with a quasi-free Hamiltonian action. We discus s in general the relation between symplectic reduction and gauging of the symplectic isometries of the sigma model action. In the case of si ngular reduction, gauging has the same effect as blowing up the singul ar point by a small amount. Using the exponential mapping of the under lying metric, we are able to construct symplectic diffeomorphisms need ed to glue the blow-up to the global reduced space which is regular, t hus providing a transition from one symplectic sigma model to another one free of singularities.