On Chiral Symmetry Breaking, Topology and Confinement

Abstract: We start with the relation between the chiral symmetry breaking and gauge field topology. New lattice result 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 $\rho,N$ decrease near $T_c$. We argue that while at $T=0$ the main contribution to the effective quark mass is chirally odd $m_{\snchi}$, near $T_c$ it rotates to chirally-even component $m_\chi$, because "infinite clusters" of topological solitons gets split into finite ones. Recent progress in understanding of topology require introduction of nonzero holonomy $<A_0>\neq 0$, which splits instantons into $N_c$ (anti)selfdual "instanton-dyons". Qualitative progress, as well as first numerical studios of the dyon ensemble are reported. New connections between chiral symmetry breaking and confinement are recently understood, since instanton-dyons generates holonomy potential with a minimum at confining value, if the ensemble is dense enough.