Magnetic Catalysis: A Review

Abstract

We give an overview of the magnetic catalysis phenomenon. In the framework of quantum field theory, magnetic catalysis is broadly defined as an enhancement of dynamical symmetry breaking by an external magnetic field. We start from a brief discussion of spontaneous symmetry breaking and the role of a magnetic field in its a dynamics. This is followed by a detailed presentation of the essential features of the phenomenon. In particular, we emphasize that the dimensional reduction plays a profound role in the pairing dynamics in a magnetic field. Using the general nature of underlying physics and its robustness with respect to interaction types and model content, we argue that magnetic catalysis is a universal and modelindependent phenomenon. In support of this claim, we show how magnetic catalysis is realized in various models with short-range and long-range interactions. We argue that the general nature of the phenomenon implies a wide range of potential applications: from certain types of solid state systems to models in cosmology, particle and nuclear physics. We finish the review with general remarks about magnetic catalysis and an outlook for future research.

Chiral and deconfinement transitions in a magnetic background using the functional renormalization group with the Polyakov loop

“…We first notice that the critical temperature increases with the magnetic field for small values of the chemical potential µ. The basic mechanism is that of magnetic catalysis [51][52][53], namely that the chiral condensate increases as a function of the magnetic field. It is interesting to note that the increase of the transition temperature as a function of B is smaller when we couple the chiral sector to the gluonic sector.…”

One-loop QCD thermodynamics in a strong homogeneous and static magnetic field

“…Using the 11-components of the quark and gluon matrix propagators from equations (2.15) and (2.19), respectively, we can obtain the 11-component of the quark self-energy matrix from the one-loop diagram (figure 1) in a strong magnetic field, 20) where 4/3 is the QCD colour factor and g is the QCD running coupling.…”

“…The remaining integration on the longitudinal loop-momentum gives the other component of the self-energy, which is, similar to the quark self-energy, separable into the vacuum and medium contributions, 20) where the trace over gamma matrices (L µν ) is calculated as…”

“…Moreover the magnetic field may be assumed uniform because even though the spatial distribution of the magnetic field is globally inhomogeneous, but in the central region of the overlapping nuclei, the magnetic field in the transverse plane varies very smoothly, which is noticed in the hadron-string simulations [9] for Au-Au collisions at √ s N N = 200 GeV with an impact parameter, b = 10 fm. Therefore, a large number of QCD related phenomena are investigated in the strong and homogeneous magnetic field, such as the chiral magnetic effect related to the generation of electric current parallel to the magnetic field due to the difference in number of right and left-handed quarks [10][11][12], the axial magnetic effect due to the flow of energy by the axial magnetic field [13,14], the chiral vortical effect due to an effective magnetic field in the rotating QGP [15,16], the magnetic catalysis and the inverse magnetic catalysis at finite temperature arising due to the breaking and the restoration of the chiral symmetry [17][18][19][20][21], the thermodynamic properties [22][23][24], the refractive indices and decay constant [25,26] of mesons in a hot magnetized medium, the conformal anomaly and the production of soft photons [27,28] at RHIC and LHC, the dispersion relation in a magnetized thermal QED [29], the synchrotron radiation [30], the dilepton production from both the weakly [31][32][33][34] and the strongly [35] coupled plasma etc.…”

Generalized Landau level representation: Effect of static screening in the quantum Hall effect in graphene

“…native scenarios utilizes the idea of magnetic catalysis (MC) [33][34][35] . The corresponding order parameters are excitonic (particle-hole) condensates responsible for the generation of the Dirac and/or Haldane masses of quasiparticles 6,[36][37][38][39][40][41][42][43] .…”