Title: Self-dual Yang-Mills and Heavenly Equations in Deformation Quantization

Speaker: Maciej Przanowski

Institution: Institute of Physics, Technical University of Lodz, Poland

Abstract

It is shown that self-dual Yang-Mills (SDYM)equations in deformation quantization can be reduced to one eqution (the master equation (ME)). Two hierarchies of conservation laws for this equation are constructed. The twistor transform and a solution to the Riemann-Hilbert problem are given.Thus ME appears to be an integrable system. Then reductions of ME to the Husain-Park (HP)heavenly equation and to sl(N,C) SDYM equation are presented. An example of a sequence of su(N) chiral fields (N>1)tending to a curved heavenly space for N tending to infinity is found. (Ward's question). This example shows that sl(N,C) or su(N) chiral fields can be considered to be in a sense fuzzy heavenly solutions.