Instanton in Euclidean non-abelian field of point-like source

Abstract

{(Anti-)instanton behaviour in Euclidean non-abelian field of the point-like source is studied by analyzing the possible (anti-)instanton deformations as resulted from the variations of its characteristic parameters. The variational principle for searching such crumpled topological configurations is formulated and the problem is resolved then algebraically by the Ritz method (multipole expansion of the deformation fields). The region of (anti-)instanton parameters relevant to the instanton liquid model is investigated in detail. The approximate efficacious method to include such configurations contributing to the appropriate partition function is proposed and verified. Evaluating average energy of Euclidean non-abelian point-like source in the instanton environment (liquid) is performed within the superposition ansatz for the corresponding solutions of the Yang-Mills equations. For the colour singlet dipole this energy escalates linearly with the separation increasing and its tension coefficient develops the magnitude commensurate with that as inferred from lattice QCD.