Phase diagram of QCD in a magnetic field: A review

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.

63 pages. 49 figures. Comments are welcome - including citation requests. version2: 65 pages. 50 figs. shuffled some material around and added some. Refs added and updated. 3rd version, fixed some refs

References in corpus (6)

• The Importance of Asymptotic Freedom for the Pseudocritical Temperature in Magnetized Quark Matter
• Quark Antiscreening at Strong Magnetic Field and Inverse Magnetic Catalysis
• Inverse magnetic catalysis in the linear sigma model with quarks
• Magnetic catalysis in nuclear matter
• Inverse Magnetic Catalysis in the three-flavor NJL model with axial-vector interaction
• Inverse magnetic catalysis and regularization in the quark-meson model

Cited by in corpus (10)

• Chiral Magnetic and Vortical Effects in High-Energy Nuclear Collisions --- A Status Report
• Holographic calculation of the QCD crossover temperature in a magnetic field
• Study of QCD Phase Diagram with Non-Zero Chiral Chemical Potential
• Inverse magnetic catalysis from the properties of the QCD coupling in a magnetic field
• Inhomogeneous chiral symmetry breaking in dense neutron-star matter
• SU(2) low energy quark effective couplings in weak external magnetic field
• Mesons in strong magnetic fields: (I) General analyses
• Critical point in the QCD phase diagram for extremely strong background magnetic fields
• Vortex solutions in the Abelian Higgs Model with a neutral scalar
• Momentum space topology of QCD