[Paper Review] Thermal monopole condensation in QCD with physical quark masses

Marco Cardinali, Massimo D’Elia+1 more|arXiv (Cornell University)|Jul 6, 2021

High-Energy Particle Collisions Research4 citations

TL;DR

This study investigates thermal monopole condensation in $N_f=2+1$ QCD at physical quark masses using lattice gauge theory. By analyzing monopole current wrappings around the thermal circle in the Maximal Abelian Gauge, it identifies a BEC-like transition at $T_{\text{BEC}} \approx 275$ MeV—significantly above the chiral crossover temperature $T_c \approx 155$ MeV—suggesting a possible non-perturbative phase transition linked to confinement dynamics.

ABSTRACT

Thermal monopoles, identified after Abelian projection as magnetic currents wrapping non-trivially around the thermal circle, are studied in $N_f = 2+1$ QCD at the physical point. The distribution in the number of wrappings, which in pure gauge theories points to a condensation temperature coinciding with deconfinement, points in this case to around 275 MeV, almost twice the QCD crossover temperature $T_c$; similar indications emerge looking for the formation of a percolating current cluster. The possible relation with other non-perturbative phenomena observed above $T_c$ is discussed.

Motivation & Objective

• To investigate whether thermal monopole condensation—a mechanism linked to dual superconductivity and confinement—occurs in full QCD with physical quark masses.
• To determine if the condensation temperature $T_{\text{BEC}}$ aligns with known phase transitions in QCD, particularly the chiral crossover at $T_c \approx 155$ MeV.
• To assess whether monopole condensation signals a distinct non-perturbative phase beyond the chiral crossover, potentially indicating an intermediate confined but chirally symmetric phase.
• To compare results with pure gauge theories and explore the role of quarks in modifying monopole dynamics and confinement mechanisms.

Proposed method

• Employ lattice QCD simulations with $N_f=2+1$ flavors at physical quark masses using the Wilson action and rooted staggered fermions.
• Apply the Maximal Abelian Gauge (MAG) projection to extract Abelian monopole currents from non-Abelian gauge configurations.
• Identify thermal monopoles as monopole currents with non-trivial winding number around the Euclidean time direction (thermal circle).
• Use the statistical distribution of multiple wrappings to reconstruct the quantum statistics of the thermal monopole ensemble and infer a BEC-like transition temperature.
• Analyze the relative weight of the largest percolating monopole current cluster as a function of temperature to detect condensation signatures.
• Compare results with pure $SU(3)$ gauge theory and other observables such as Polyakov loop susceptibilities, quark number susceptibilities, and topological charge distributions.

Experimental results

Research questions

• RQ1 Does thermal monopole condensation occur in full QCD with physical quark masses, and at what temperature?
• RQ2 How does the inferred $T_{\text{BEC}}$ from monopole wrappings compare to the chiral crossover temperature $T_c \approx 155$ MeV and the pure gauge deconfinement transition?
• RQ3 Is the observed monopole condensation associated with a true phase transition, or is it a crossover-like feature without strong thermodynamic signatures?
• RQ4 How do monopole dynamics and clustering evolve in the temperature range above $T_c$, and do they correlate with other non-perturbative phenomena such as instanton-dyons or stringy fluid behavior?
• RQ5 To what extent is the monopole condensation temperature sensitive to quark mass and flavor content, and does it signal a new phase of matter?

Key findings

• The thermal monopole condensation temperature $T_{\text{BEC}}$ is found to be approximately 275 MeV, significantly above the chiral crossover temperature $T_c \approx 155$ MeV.
• The distribution of monopole wrappings and the emergence of a percolating current cluster both indicate a sharp transition-like behavior at $T_{\text{BEC}} \approx 275$ MeV.
• The monopole density normalized to the pure gauge case shows a distinct drop around $T_{\text{BEC}}$, suggesting a strong suppression of monopole excitations at this scale.
• The condensation temperature $T_{\text{BEC}}$ is strikingly close to the pure gauge $T_c$ for $SU(3)$, though the physical mechanism may differ due to explicit chiral symmetry breaking.
• The observed monopole condensation is not accompanied by strong signatures in standard thermodynamic observables like the Polyakov loop or quark number susceptibility, indicating it may be a hidden non-perturbative feature.
• The results are consistent with other hints of non-perturbative physics above $T_c$, such as slow approach to DIGA behavior in topological charge distributions and possible intermediate phases like the stringy fluid or instanton-dyons.