On top Chern classes of universal bundles on moduli spaces of rank two coherent sheaves on the projective plane, or How to calculate the correlation function in SYM N=2 Nf=4 quantum field theory on complex projective plane

Abstract

We explain how to calculate the correlation function for SYM N=2 SO(3)-gauge QFT with 4 flavors in terms of top Chern classes of the universal bundles over the moduli spaces of rank 2 stable torsion free coherent sheaves with det=-1 on the complex projective plane. We give a direct geometrical description of these moduli spaces, study a 2-dimensional torus action on them, and calculate several initial coefficients of the correlation function via Bott residue formula.