Inverse magnetic catalysis and the Polyakov loop (1303.3972v2)

Abstract: We study the physical mechanism of how an external magnetic field influences the QCD quark condensate. Two competing mechanisms are identified, both relying on the interaction between the magnetic field and the low quark modes. While the coupling to valence quarks enhances the condensate, the interaction with sea quarks suppresses it in the transition region. The latter `sea effect' acts by ordering the Polyakov loop and, thereby, reduces the number of small Dirac eigenmodes and the condensate. It is most effective around the transition temperature, where the Polyakov loop effective potential is flat and a small correction to it by the magnetic field can have a significant effect. Around the critical temperature, the sea suppression overwhelms the valence enhancement, resulting in a net suppression of the condensate, named inverse magnetic catalysis. We support this physical picture by lattice simulations including continuum extrapolated results on the Polyakov loop as a function of temperature and magnetic field. We argue that taking into account the increase in the Polyakov loop and its interaction with the low-lying modes is essential to obtain the full physical picture, and should be incorporated in effective models for the description of QCD in magnetic fields in the transition region.

• The paper identifies two competing mechanisms where valence enhancement boosts the quark condensate while sea quark interactions suppress it near the critical temperature.
• Lattice simulations demonstrate that magnetic fields increase the spectral density of the Dirac operator at low temperatures and reduce it during the crossover phase.
• The study shows that the ordering of the Polyakov loop via magnetic effects is crucial, suggesting that QCD models must include these interactions for accurate extreme environment predictions.

Inverse Magnetic Catalysis and the Polyakov Loop

The paper explores the intricate mechanisms by which external magnetic fields influence the quark condensate in Quantum Chromodynamics (QCD), especially around the transition temperature. The authors identify two competing mechanisms: while the interaction with valence quarks tends to enhance the quark condensate, the interaction with sea quarks leads to its suppression—a phenomenon named inverse magnetic catalysis.

Key Mechanisms

The paper uncovers that the external magnetic field affects chiral symmetry breaking through two distinct paths:

1. Valence Mechanism: This mechanism is responsible for magnetic catalysis at zero temperature, where the magnetic field enhances the spectral density of the Dirac operator, thus boosting the condensate. This effect persists even in the quenched approximation and is largely independent of the quark masses.
2. Sea Mechanism: Most significant around the crossover temperature, this mechanism reduces the condensate. It influences the sampling of gauge fields by affecting the quark determinant, and thus effectively orders the Polyakov loop. This ordering diminishes the presence of small Dirac eigenmodes, resulting in the suppression of the quark condensate versus its enhancement by valence quarks.

Computational and Numerical Insights

Lattice simulations form the empirical foundation of this research, supporting the theoretical insight into these mechanisms. The paper elaborated on how lattice simulations reveal lattice artifact corrections and the necessity for finer computational grids with appropriately tuned quark masses to capture these effects accurately. The paper emphasizes that the indirect impact of magnetic fields on gauge degrees of freedom through quarks is crucial in the transition region.

Implications and Future Considerations

These findings imply that the interaction between the Polyakov loop and the low-lying Dirac modes is essential for a nuanced understanding of QCD in the presence of magnetic fields during the transition phase. The paper suggests that effective models of QCD should incorporate these interactions to provide reliable descriptions of the system, particularly in scenarios involving magnetic fields.

The complex interplay between valence enhancement and sea suppression around the transition temperature could have broader ramifications for understanding strong-interaction matter in extreme environments, such as neutron stars and heavy-ion collisions. The sensitivity of many critical QCD processes to the presence of magnetic fields underscores the need for models that accurately incorporate these effects.

The paper conjectures that the sea effect's dependence on quark masses implies that lighter quarks would accentuate inverse magnetic catalysis, suggesting a delicate balance that could become more pronounced closer to the chiral limit. As the lattice data indicates a return to magnetic catalysis at higher temperatures, further investigations could refine these boundary conditions and contribute to developing a cohesive picture of QCD under various external influences.

Conclusion

The paper provides a sophisticated analysis of QCD's response to external magnetic fields, highlighting the necessity to incorporate these effects in theoretical models. The dual mechanisms identified—valence enhancement and sea suppression—offer crucial insights into the behavior of QCD matter at critical thresholds, paving the way for refined modeling techniques and understanding of strong-interaction physics under extreme conditions.