Applications of instantons, sphalerons and instanton-dyons in QCD

I start with a general map of gauge topology, including monopoles, instantons and instanton-dyons. Then comes reminder of the “topological landscape”, the minimal energy gauge field configurations, as a function of Chern-Simons number Ncs and r.m.s. size. It includes “valleys” at integer Ncs separated by mountain ridges. The meaning of instantons, instanton-antiinstanton “streamlines” or thimbles, and sphalerons are reminded, together with some proposal to produce sphalerons at LHC and RHIC.

Applications of instanton ensembles, as a model of QCD vacuum, are mostly related to their fermionic zero modes and t’Hooft effective Lagrangian, which explains explicit and spontaneous breaking of chiral symmetries. Recent applications are related with hadronic wave functions, at rest and in the light front (LFWFs). Two application would be spin-dependent forces and  the so called “flavor asymmetry of antiquark sea” of the nucleons. At temperatures comparable to deconfinement transition, instantons get split into constituents called instanton-dyons. Studies of their ensemble explains both deconfinement and chiral transitions, in ordinary and deformed QCD.

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