 Magnetic catalysis

Magnetic catalysis is a phenomenon in quantum field theory which explains a spontaneous breaking of flavor or chiral symmetry, triggered by the presence of an external magnetic field.
Contents
General description
The underlying mechanism behind the magnetic catalysis^{[1]} is the dimensional reduction of the lowenergy charged spin1/2 particles and, as a result of such reduction, a strong enhancement of the particleantiparticle pairing responsible for symmetry breaking. For gauge theories in 3+1 dimensions, such as quantum electrodynamics and quantum chromodynamics, the dimensional reduction leads to an effective (1+1)dimensional lowenergy dynamics as if the spacetime were (1+1)dimensional. (Here the dimensionality of spacetime is written as D+1, where D stands for the number of spacelike directions and 1 stands for a single timelike direction.) In simple terms, the dimensional reduction reflects the fact that the motion of charged particles is (partially) restricted in the two spacelike directions perperndicular to the magnetic field. However, this orbital motion constraint alone is not sufficient (for example, there is no dimensional reduction for charged scalar particles, carrying spin 0, although their orbital motion is constrained in the same way.) It is also important that fermions have spin 1/2 and, as follows from the Atiyah–Singer index theorem, their lowest Landau level states have an energy independent of the magnetic field. (The corresponding energy vanishes in the case of massless particles.) This is in contrast to the energies in the higher Landau levels, which are proportional to the square root of the magnetic field. Therefore, if the field is sufficiently strong, only the lowest Landau level states are dynamically accessible at low energies. The states in the higher Landau levels decouple and become almost irrelevant. The phenomenon of magnetic catalysis has applications in particle physics, nuclear physics and condensed matter physics.
Possible applications
Chiral symmetry breaking in quantum chromodynamics
In the theory of quantum chromodynamics, magnetic catalysis can be applied when quark matter is subject to extremely strong magnetic fields.^{[2]} Such strong magnetic fields can lead to more pronounced effects of chiral symmetry breaking, e.g., lead to (i) a larger value of the chiral condensate, (ii) a larger dynamical (constituent) mass of quarks, (iii) larger baryon masses, (iv) modified pion decay constant, etc.
Recently, there was an increased activity to crosscheck the effects of magnetic catalysis in the limit of a large number of colors, using the technique of AdS/CFT correspondence. Again, in this framework, the universality of the effect withstood the test.
Cosmology
There were a few studies suggesting that magnetic catalysis may play a crucial role in the Early Universe when there existed superstrong primodial magnetic fields. The magnetic catalysis may then affect the dynamics of the electroweak phase transition.
Condensed matter physics
It seems very natural to test the ideas of magnetic catalysis in applications to many field theories used in tudies of condensed matter systems.
Quantum Hall effect in graphene
The idea of magnetic catalysis can be used to explain the observation of new quantum Hall plateaux in graphene in strong magnetic fields beyond the standard anomalous sequence at filling factors ν=4(n+½) where n is an integer. The additional quantum Hall plataues develop at ν=0, ν=±1, ν=±3 and ν=±4.
The mechanism of magnetic catalysis in a relativisticlike planar systems such as graphene is very natural. In fact, it was originally proposed for a 2+1 dimensional model^{[1]}, which is almost the same as the lowenergy effective theory of graphene written in terms of massless Dirac fermions.^{[3]} In application to a single layer of graphite (i.e., graphene), magnetic catalysis triggers the breakdown of an approximate internal symmetry and, thus, lifts the 4fold degeneracy of Landau levels.^{[4]}^{[5]}
References
 ^ ^{a} ^{b} V.P. Gusynin, V.A. Miransky, I.A. Shovkovy, Phys. Rev. Lett. 73 (1994) 34993502, hepph/9405262
 ^ V.A. Miransky and I.A. Shovkovy, Phys. Rev. D 66 (2002) 045006, hepph/0205348
 ^ G. W. Semenoff, Phys. Rev. Lett. 53, 2449–2452 (1984)
 ^ D. V. Khveshchenko, Phys. Rev. Lett. 87, 206401 (2001), condmat/0106261
 ^ E. V. Gorbar, V. P. Gusynin, V. A. Miransky, and I. A. Shovkovy, Phys. Rev. B 66, 045108 (2002), condmat/0202422
External links
 Articles on Magnetic catalysis at http://scholar.google.com/
 Magnetic catalysis in graphene
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