Broken Valence Chiral Symmetry and Chiral Polarization of Dirac Spectrum in N$_f$=12 QCD at Small Quark Mass

TL;DR

This study investigates the relationship between valence chiral symmetry breaking and chiral polarization in twelve-flavor QCD, revealing different regimes of symmetry behavior and implications for the conformal window.

Contribution

It provides the first detailed analysis of vSChSB and ChP equivalence in Nf=12 QCD and identifies multiple regimes of chiral symmetry behavior at different quark masses.

Findings

vSChSB-ChP correspondence holds in studied systems

Existence of a critical mass m_c separating different spectral behaviors

Potential valence chiral symmetry restoration at very small quark masses

Abstract

The validity of recently proposed equivalence between valence spontaneous chiral symmetry breaking (vSChSB) and chiral polarization of low energy Dirac spectrum (ChP) in SU(3) gauge theory, is examined for the case of twelve mass-degenerate fundamental quark flavors. We find that the vSChSB-ChP correspondence holds for regularized systems studied. Moreover, our results suggest that vSChSB occurs in two qualitatively different circumstances: there is a quark mass $m_c$ such that for $m > m_c$ the mode condensing Dirac spectrum exhibits standard monotonically increasing density, while for $m_{ch} < m < m_c$ the peak around zero separates from the bulk of the spectrum, with density showing a pronounced depletion at intermediate scales. Valence chiral symmetry restoration may occur at yet smaller masses $m < m_{ch}$, but this has not yet been seen by overlap valence probe, leaving the $m_{ch}=0$ possibility open. The latter option could place massless N$_f$=12 theory outside of conformal window. Anomalous behavior of overlap Dirac spectrum for $m_{ch} < m < m_c$ is qualitatively similar to one observed previously in zero and few-flavor theories as an effect of thermal agitation.