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 $m_{\text{snchi}}$, 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 $<A_0>\ne 0$, 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.

Comments: Written contribution to proceedings of Memorial conference for Prof.Gerald E. Brown, (Stony Brook, November 2013), to appear in a special volume of Nucl.Phys.A