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 Λch. Here we consider more general association involving the low-energy layer of chirally polarized modes which, in addition to its width (Λch), is also characterized by volume density of participating modes (Ω) and the volume density of total chirality (Ωch). Few possible forms of the correspondence are discussed, paying particular attention to singular cases where Ω 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 Nf=0 QCD) and light quarks (inNf=12), both in the regime of possible symmetry restoration, and find agreement with these ideas. In Nf=0 QCD, results from several volumes indicate that, at the lattice cutoff studied, the deconfinement temperature Tc is strictly smaller than the overlap–valence chiral transition temperature Tch in real Polyakov line vacuum. Somewhat similar intermediate phase (in quark mass) is also seen in Nf=12. It is suggested that deconfinement in Nf=0 is related to indefinite convexity of absolute X-distributions.

Document Type


Publication Date


Notes/Citation Information

Published in Nuclear Physics B, v. 891, p. 1-41.

©2014 The Authors.

Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/3.0/).

Digital Object Identifier (DOI)


Funding Information

Funded by SCOAP3.