Phase diagram of QCD in a magnetic field: A review (1411.7176v3)

Abstract: We review in detail recent advances in our understanding of the phase structure and the phase transitions of hadronic matter in strong magnetic fields $B$ and zero quark chemical potentials $\mu_f$. Many aspects of QCD are described using low-energy effective theories and models such as the MIT bag model, the hadron resonance gas model, chiral perturbation theory, the Nambu-Jona-Lasinio (NJL) model, the quark-meson (QM) model and Polyakov-loop extended versions of the NJL and QM models. We critically examine their properties and applications. This includes mean-field calculations as well as approaches beyond the mean-field approximation such as the functional renormalization group (FRG). Renormalization issues are discussed and the influence of the vacuum fluctuations on the chiral phase transition is pointed out. Magnetic catalysis at $T=0$ is covered as well. We discuss recent lattice results for the thermodynamics of nonabelian gauge theories with emphasis on $SU(2)_c$ and $SU(3)_c$. In particular, we focus on inverse magnetic catalysis around the transition temperature $T_c$ as a competition between contributions from valence quarks and sea quarks resulting in a decrease of $T_c$ as a function of $B$. Finally, we discuss recent efforts to modify models in order to reproduce the behavior observed on the lattice.

Overview of QCD Phase Diagram in a Magnetic Field

This paper offers a comprehensive review of recent developments in understanding the phase diagram of Quantum Chromodynamics (QCD) when subjected to strong magnetic fields and zero quark chemical potentials. The authors utilize various effective models and theories, including the MIT bag model, Nambu-Jona-Lasinio (NJL) model, quark-meson model, and Polyakov-loop extensions, to dissect the complex behaviors and phase transitions of hadronic matter under these conditions.

Topics Explored:

1. Effective Models and Theories: The paper delves deep into the constructs of effective models such as the chiral perturbation theory. These models help understand low-energy QCD without exploring the intricacies of the underlying theory. The authors discuss renormalization, vacuum fluctuations, and mean-field calculations while also exploring beyond mean-field approaches like the functional renormalization group.
2. Magnetic Catalysis at $T = 0$: A distinctive feature identified is the phenomenon of magnetic catalysis. At zero temperature, the presence of a strong magnetic field can enhance or induce chiral symmetry breaking, thereby influencing the quark condensate properties. This observation is pivotal in understanding the characteristics prevalent in noncentral heavy-ion collisions, compact stars, and the early universe.
3. Lattice Results: The paper also juxtaposes recent lattice results focusing on thermodynamics of nonabelian gauge theories, emphasizing $SU(2)_c$ and $SU(3)_c$ frameworks. Within this context, inverse magnetic catalysis—where the chiral transition temperature decreases as a function of $B$—is discussed as influenced by valence and sea-quark contributions.
4. Phase Transitions: A thorough examination of phase transitions in QCD is conducted, highlighting the competition between contributions from valence and sea quarks which result in a decrease of the transition temperature $T_c$ as a function of $B$.
5. Implications and Future Directions: Practical and theoretical implications are evident for the early universe and astrophysical phenomena exhibiting strong magnetic fields. The review anticipates further advancements and refinement of current models to incorporate magnetic influences more effectively.

Numerical Results and Bold Claims:

The authors present numerical results that elucidates strong findings such as the decrease in $T_c$ around transition temperatures due to inverse magnetic catalysis. These results challenge conventional understanding and demand a nuanced approach to considering magnetic field impact in QCD systems.

Speculative Future in AI Developments:

Although AI is not the primary focus, the paper suggests an interdisciplinary approach, leveraging AI for conducting complex calculations and simulations in QCD research.

Overall, this review is an invaluable resource for those exploring QCD phase transitions in magnetic fields. It methodically addresses the nuances and challenges posed by the magnetic field in hadronic matter, paving the way for future explorations in this area.