Chiral polarization scale of QCD vacuum and spontaneous chiral symmetry breaking

It has recently been found that dynamics of pure glue QCD supports the low energy band of Dirac modes with local chiral properties qualitatively different from that of a bulk: while bulk modes suppress chirality relative to statistical independence between left and right, the band modes enhance it. The width of such chirally polarized zone - chiral polarization scale Lambda_ch - has been shown to be finite in the continuum limit at fixed physical volume. Here we present evidence that Lambda_ch remains non-zero also in the infinite volume, and is therefore a dynamical scale in the theory. Our experiments in N_f=2+1 QCD support the proposition that the same holds in the massless limit, connecting Lambda_ch to spontaneous chiral symmetry breaking. In addition, our results suggest that thermal agitation in quenched QCD destroys both chiral polarization and condensation of Dirac modes at the same temperature T_ch > T_c.Comment: 5 pages, 4 figures. Proceedings of "Extreme QCD" workshop, Washington, DC, Aug 21-23 201

QCD at imaginary chemical potential with Wilson fermions

We investigate the phase diagram in the temperature, imaginary chemical potential plane for QCD with three degenerate quark flavors using Wilson type fermions. While more expensive than the staggered fermions used in past studies in this area, Wilson fermions can be used safely to simulate systems with three quark flavors. In this talk, we focus on the (pseudo)critical line that extends from $\mu=0$ in the imaginary chemical potential plane, trace it to the Roberge-Weiss line, and determine its location relative to the Roberge-Weiss transition point. In order to smoothly follow the (pseudo)critical line in this plane we perform a multi-histogram reweighting in both temperature and chemical potential. To perform reweighting in the chemical potential we use the compression formula to compute the determinants exactly. Our results are compatible with the standard scenario.Comment: 7 pages, 5 figures. Proceedings of the 31st International Symposium on Lattice Field Theory (Lattice 2013), 29 July - 3 August 2013, Mainz, German

Chiral Symmetry Breaking and Chiral Polarization: Tests for Finite Temperature and Many Flavors

It was recently conjectured that, in SU(3) gauge theories with fundamental quarks, valence spontaneous chiral symmetry breaking is equivalent to condensation of local dynamical chirality and appearance of chiral polarization scale $\Lambda_{ch}$. Here we consider more general association involving the low-energy layer of chirally polarized modes which, in addition to its width ($\Lambda_{ch}$), is also characterized by volume density of participating modes ($\Omega$) and the volume density of total chirality ($\Omega_{ch}$). Few possible forms of the correspondence are discussed, paying particular attention to singular cases where $\Omega$ emerges as the most versatile characteristic. The notion of finite-volume "order parameter", capturing the nature of these connections, is proposed. We study the effects of temperature (in N$_f$=0 QCD) and light quarks (in N$_f$=12), both in the regime of possible symmetry restoration, and find agreement with these ideas. In N$_f$=0 QCD, results from several volumes indicate that, at the lattice cutoff studied, the deconfinement temperature $T_c$ is strictly smaller than the overlap-valence chiral transition temperature $T_{ch}$ in real Polyakov line vacuum. Somewhat similar intermediate phase (in quark mass) is also seen in N$_f$=12. It is suggested that deconfinement in N$_f$=0 is related to indefinite convexity of absolute X-distributions.Comment: 45 pages, 20 figures; v2: reduced the size of submission and fixed references to appendices; v3: minor changes - published for

Phases of SU(3) Gauge Theories with Fundamental Quarks via Dirac Spectral Density

We propose that, in SU(3) gauge theories with fundamental quarks, confinement can be inferred from spectral density of the Dirac operator. This stems from the proposition that its possible behaviors are exhausted by three distinct types (Fig.1). The monotonic cases are standard and entail confinement with valence chiral symmetry breaking (A) or the lack of both (C,C'). The bimodal (anomalous) option (B) was frequently regarded as an artifact (lattice or other) in previous studies, but we show for the first time that it persists in the continuum limit, and conclude that it informs of a non-confining phase with broken valence chiral symmetry. This generalization rests on the following. $(\alpha)$ We show that bimodality in $N_f$=0 theory past deconfinement temperature $T_c$ is stable with respect to removal of both infrared and ultraviolet cutoffs, indicating that anomalous phase is not an artifact. $(\beta)$ We demonstrate that transition to bimodality in $N_f$=0 is simultaneous with the loss of confinement: anomalous phase occurs for $T_c < T < T_{ch}$, where $T_{ch}$ is the valence chiral restoration temperature. $(\gamma)$ Evidence is presented for thermal anomalous phase in $N_f$=2+1 QCD at physical quark masses, whose onset too coincides with the conventional "crossover $T_c$''. We conclude that the anomalous regime $T_c < T < T_{ch}$ is very likely a feature of nature's strong interactions. $(\delta)$ Our past studies of zero-temperature $N_f$=12 theories revealed that bimodality also arises via purely light-quark effects. As a result, we expect to encounter anomalous phase on generic paths to valence chiral restoration. We predict its existence also for $N_f$ massless flavors ($T=0$) in the range $N_f^c < N_f < N_f^{ch}$, where $N_f^c$ could be quite low. Conventional arguments would associate $N_f^{ch}$ with the onset of conformal window.Comment: 10 pages, 6 figures; v2: PRD version, few remarks/references added and minor reformulations made, 11 pages, 6 figure