Gauging and symplectic blowing up in nonlinear sigma-models: I. point singularities

Details Gauging and symplectic blowing up in nonlinear sigma-models: I. point singularities Gauging and symplectic blowing up in nonlinear sigma-models: I. point singularities

1993-10-07

arxiv.org/abs/hep-th/9310037v2

Z.Phys. C67 (1995) 351-363

Physics

High Energy Physics

High Energy Physics - Theory

32 pages, LaTex, THEP 93/24 (corrected and expanded(about 5 pages) version)

Scientific paper

10.1007/BF01571298

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

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