[Paper Review] Deconfinement, Chiral Symmetry Breaking and Chiral Polarization

Andrei Alexandru, Ivan Horváth|arXiv (Cornell University)|Sep 24, 2014

Quantum Chromodynamics and Particle Interactions8 references3 citations

TL;DR

This paper investigates the existence of a deconfined, chirally broken phase in Nf=0 QCD at temperatures above the deconfinement transition (Tc < T < Tch), using finite-volume lattice simulations with overlap fermions. It demonstrates that valence chiral symmetry breaking is accompanied by dynamical chiral polarization of Dirac eigenmodes, with the vSChSB–ChP correspondence robustly preserved across lattice spacings (a = 0.085 fm and a = 0.060 fm), indicating the anomalous phase persists toward the continuum limit.

ABSTRACT

We examine the feasibility of the proposition that there is a temperature range T$_c$ &lt; T &lt; T$_{ch}$ in N$_f$=0 QCD, where real Polyakov line (deconfined) vacuum exhibits valence spontaneous chiral symetry breaking and dynamical chiral polarization of Dirac eigenmodes. Detailed finite-volume analysis convincingly demonstrates the existence of such phase at fixed cutoff (a=0.085 fm). Moreover, it is found that this behavior also takes place closer to the continuum limit (a=0.060 fm) without qualitative change in its properties.

Motivation & Objective

• To test whether a deconfined, chirally broken phase exists in Nf=0 QCD above Tc, where the Polyakov loop is non-zero but chiral symmetry remains spontaneously broken.
• To verify the validity of the vSChSB–ChP correspondence in this anomalous phase using dynamical chiral polarization as a probe.
• To assess whether the observed behavior is a lattice artifact by examining the system at finer lattice spacings approaching the continuum limit.
• To determine if the chiral polarization layer, characterized by volume density Ω, persists under continuum extrapolation.

Proposed method

• Finite-volume lattice simulations with Wilson gauge action and overlap Dirac operator (ρ=26/19) at fixed scale r0=0.5 fm.
• Use of the overlap fermion formulation to probe valence chiral symmetry breaking via near-zero mode density ρ(λ→0).
• Definition of chiral polarization via correlation coefficient CA for each Dirac mode, enabling construction of cumulative polarization density σch(σ).
• Analysis of σch(σ) to detect the presence of a chirally polarized layer, with Ω defined as the maximum of σch(σ) at small σ.
• Comparison of spectral density ρ(λ) and σch(σ) across different lattice spacings (a=0.085 fm and a=0.060 fm) at fixed T/Tc=1.12.
• Volume scaling analysis of Ω to assess convergence in the infinite-volume limit.

Experimental results

Research questions

• RQ1 Does a deconfined, chirally broken phase exist in Nf=0 QCD above Tc, with a real Polyakov line and non-zero valence chiral condensate?
• RQ2 Is the vSChSB–ChP correspondence preserved in this anomalous phase, as indicated by chiral polarization of low-lying Dirac modes?
• RQ3 Does the anomalous behavior in ρ(λ) and σch(σ) persist when approaching the continuum limit with finer lattice spacing?
• RQ4 Is the observed chiral polarization robust under volume and cutoff variation, indicating a physical phase rather than a lattice artifact?

Key findings

• The anomalous phase with deconfinement and spontaneous valence chiral symmetry breaking exists at a=0.085 fm, as confirmed by non-monotonic near-zero mode density ρ(λ) and non-zero Ω.
• The chiral polarization layer, quantified by Ω, increases monotonically with spatial volume, supporting the existence of a thermodynamically stable phase.
• At a=0.060 fm (T/Tc=1.12), the spectral density ρ(λ) near zero remains anomalously peaked, with no significant reduction in peak height, indicating persistence of near-zero modes.
• The cumulative chiral polarization σch(σ) shows a clear positive bump at small σ, confirming the presence of a chirally polarized layer in the continuum limit.
• The value of Ω decreases slightly at finer lattice spacing, but this is attributed to reduced peak width rather than weakened polarization, indicating no qualitative change in chiral dynamics.
• The vSChSB–ChP correspondence holds robustly across both lattice spacings, supporting a deep connection between chiral symmetry breaking and chiral polarization in the anomalous phase.