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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 $<A_0> eq 0$, 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.
We demonstrate that $SO(N_{c})$ gauge theories with matter fields in the vector representation confine due to monopole condensation and break the $SU(N_{F})$ chiral symmetry to $SO(N_{F})$ via the quark bilinear. Our results are obtained by perturbin
We study the relation between quark confinement and chiral symmetry breaking in QCD. Using lattice QCD formalism, we analytically express the various confinement indicators, such as the Polyakov loop, its fluctuations, the Wilson loop, the inter-quar
The spontaneous breaking of chiral symmetry is examined by chiral effective theories, such as the linear sigma model and the Nambu Jona-Lasinio (NJL) model. Indicating that sufficiently large contribution of the UA(1) anomaly can break chiral symmetr
We establish that QED3 can possess a critical number of flavours, N_f^c, associated with dynamical chiral symmetry breaking if, and only if, the fermion wave function renormalisation and photon vacuum polarisation are homogeneous functions at infrare
We study the phase diagram of QCD with the help of order parameters for chiral symmetry breaking and quark confinement. We also introduce a new order parameter for the confinement phase transition, which is related to the quark density. It is easily