V. A. Miransky

Quantum field theory in a magnetic field: From quantum chromodynamics to graphene and Dirac semimetals

A range of quantum field theoretical phenomena driven by external magnetic fields and their applications in relativistic systems and quasirelativistic condensed matter ones, such as graphene and Dirac/Weyl semimetals, are reviewed. We start by introducing the underlying physics of the magnetic catalysis. The dimensional reduction of the low-energy dynamics of relativistic fermions in an external magnetic field is explained and its role in catalyzing spontaneous symmetry breaking is emphasized. The general theoretical consideration is supplemented by the analysis of the magnetic catalysis in quantum electrodynamics, chromodynamics and quasirelativistic models relevant for condensed matter physics. By generalizing the ideas of the magnetic catalysis to the case of nonzero density and temperature, we argue that other interesting phenomena take place. The chiral magnetic and chiral separation effects are perhaps the most interesting among them. In addition to the general discussion of the physics underlying chiral magnetic and separation effects, we also review their possible phenomenological implications in heavy-ion collisions and compact stars. We also discuss the application of the magnetic catalysis ideas for the description of the quantum Hall effect in monolayer and bilayer graphene, and conclude that the generalized magnetic catalysis, including both the magnetic catalysis condensates and the quantum Hall ferromagnetic ones, lies at the basis of this phenomenon. We also consider how an external magnetic field affects the underlying physics in a class of three-dimensional quasirelativistic condensed matter systems, Dirac semimetals. While at sufficiently low temperatures and zero density of charge carriers, such semimetals are expected to reveal the regime of the magnetic catalysis, the regime of Weyl semimetals with chiral asymmetry is realized at nonzero density...

Dimensional reduction and dynamical chiral symmetry breaking by a magnetic field in (3+1)-dimensions

Abstract It is shown that in 3 + 1 dimensions, a constant magnetic field is a catalyst of dynamical chiral symmetry breaking, leading to the generation of a fermion mass even at the weakest attractive interaction between fermions. The essence of this effect is the dimensional reduction D → D − 2(3 + 1 → 1 + 1) in the dynamics of fermion pairing in a magnetic field. The effect is illustrated in the Nambu-Jona-Lasinio model. Possible applications of this effect are briefly discussed.

Magnetic catalysis and anisotropic confinement in QCD

The expressions for dynamical masses of quarks in the chiral limit in QCD in a strong magnetic field are obtained. A low energy effective action for the corresponding Nambu-Goldstone bosons is derived and the values of their decay constants as well as the velocities are calculated. The existence of a threshold value of the number of colors

Dynamical chiral symmetry breaking by a magnetic field in QED

{N}_{c}^{\mathrm{thr}},

Spontaneous symmetry breaking with abnormal number of Nambu-Goldstone bosons and kaon condensate

dividing the theories with essentially different dynamics, is established. For the number of colors

Theory of the magnetic catalysis of chiral symmetry breaking in QED

{N}_{c}\ensuremath{\ll}{N}_{c}^{\mathrm{thr}},

Dynamical chiral symmetry breaking on a brane in reduced QED

an anisotropic dynamics of confinement with the confinement scale much less than

Gluonic phase in neutral two-flavor dense QCD

{\ensuremath{\Lambda}}_{\mathrm{QCD}}

Engineering Weyl nodes in Dirac semimetals by a magnetic field

and a rich spectrum of light glueballs is realized. For

Dynamics in the quantum Hall effect and the phase diagram of graphene

{N}_{c}