Affine A3(1) 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 a plane fields are holomorphic, but the right outgoing SD β plane fields are antiholomorphic, meanwhile the diffeomorphism symmetry is preserved with mutual inverse affine rapidity parameters μ and 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 conformal 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 we establish the algebra for the 't Hooft–Hecke operators in the Hecke correspondence of the geometric Langlands program.