Affine A^{(1)}_{3} N=2 monopole as the D module and affine ADHMN sheaf

Abstract

A Higgs-Yang Mills monopole scattering spherical symmetrically along light cones is given. The left incoming anti-self-dual αplane fields are holomorphic, but the right outgoing SD βplane fields are antiholomorphic, meanwhile the diffeomorphism symmetry is preserved with mutual inverse affine rapidity parameters μand μ^{-1}. The Dirac wave function scattering in this background also factorized respectively into the (anti)holomorphic amplitudes. The holomorphic anomaly is realized by the center term of a quasi Hopf algebra corresponding to an integrable conform affine massive field. We find explicit Nahm transformation matrix(Fourier-Mukai transformation) between the Higgs YM BPS (flat) bundles (D modules) and the affinized blow up ADHMN twistors (perverse sheafs). Thus establish the algebra for the Hecke-'t Hooft operators in the Hecke correspondence of the geometric Langlands Program.