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

TL;DR

This paper explores the mathematical structure of monopole scattering in a Higgs-Yang Mills theory, revealing connections to affine algebraic geometry, D-modules, and the geometric Langlands Program.

Contribution

It introduces an explicit Nahm transformation linking Higgs YM BPS bundles with affine ADHMN sheaves, advancing the understanding of algebraic structures in gauge theories.

Findings

Explicit Nahm transformation matrix derived

Holomorphic and antiholomorphic plane fields characterized

Connection established with Hecke-'t Hooft operators

Abstract

A Higgs-Yang Mills monopole scattering spherical symmetrically along light cones is given. The left incoming anti-self-dual \alpha plane fields are holomorphic, but the right outgoing SD \beta plane fields are antiholomorphic, meanwhile the diffeomorphism symmetry is preserved with mutual inverse affine rapidity parameters \mu and \mu^{-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.