On chiral symmetry breaking, topology and confinement

We start with the relation between the chiral symmetry breaking and gauge field topology. New lattice results further enhance the notion of Zero Mode Zone, a very narrow strip of states with quasizero Dirac eigenvalues. Then we move to the issue of “origin of mass” and Brown–Rho scaling: a number of empirical facts contradicts to the idea that masses of quarks and such hadrons as ρ,Nρ,N decrease near TcTc. We argue that while at T=0T=0 the main contribution to the effective quark mass is chirally odd mχ̸mχ̸, near TcTc it rotates to chirally-even component mχmχ, because “infinite clusters” of topological solitons gets split into finite ones. Recent progress in understanding of topology require introduction of nonzero holonomy 〈A0〉≠0〈A0〉≠0, which splits instantons into NcNc (anti)selfdual “instanton–dyons”. Qualitative progress, as well as first numerical studies of the dyon ensemble are reported. New connections between chiral symmetry breaking and confinement are recently understood, since instanton–dyons generate holonomy potential with a minimum at confining value, if the ensemble is dense enough.