http://inspirehep.net/record/1347138/files/arXiv:1503.00732.pdf

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

The Chiral Magnetic Effect (CME) is the phenomenon of electric charge separation along the external magnetic field that is induced by the chirality imbalance. The CME is a macroscopic quantum effect - it is a manifestation of the chiral anomaly creating a collective motion in Dirac sea. Because the chirality imbalance is related to the global topology of gauge fields, the CME current is topologically protected and hence non-dissipative even in the presence of strong interactions. As a result, the CME and related quantum phenomena affect the hydrodynamical and transport behavior of systems possessing chiral fermions, from the quark-gluon plasma to chiral materials. The goal of the present review is to provide an elementary introduction into the main ideas underlying the physics of CME, a historical perspective, and a guide to the rapidly growing literature on this topic.

The Chiral Magnetic Effect and Anomaly-Induced Transport

We consider a relativistic plasma containing charged chiral fermions in an external magnetic field, e.g a chirally symmetric quark-gluon plasma created in relativistic heavy ion collisions. We show that triangle anomalies imply the existence of a new type of collective gapless excitation in this system that stems from the coupling between the density waves of the electric and chiral charges; we call it ”the Chiral Magnetic Wave” (CMW). The CMW exists even in a neutral plasma, i.e. in the absence of the axial and vector chemical potentials. We demonstrate the existence of CMW and study its properties using three different approaches: i) relativistic magnetohydrodynamics; ii) dimensional reduction to (1 + 1) Sine-Gordon model, appropriate in a strong magnetic field; and iii) holographic QCD (Sakai-Sugimoto model), appropriate at strong coupling. We also briefly discuss the phenomenological implications of the CMW for heavy ion collisions.

Chiral Magnetic Wave

The hot and dense matter generated in heavy-ion collisions may contain domains which are not invariant under P and CP transformations. Moreover, heavy-ion collisions can generate extremely strong magnetic fields as well as electric fields. The interplay between the electromagnetic field and triangle anomaly leads to a number of macroscopic quantum phenomena in these P- and CP-odd domains known as anomalous transports. The purpose of this article is to give a pedagogical review of various properties of the electromagnetic fields, the anomalous transport phenomena, and their experimental signatures in heavy-ion collisions.

https://iopscience.iop.org/article/10.1088/0034-4885/79/7/076302/pdf

Electromagnetic fields and anomalous transports in heavy-ion collisions-a pedagogical review.

We analyze a holographic model with a pure gauge and a mixed gauge-gravitational Chern-Simons term in the action. These are the holographic implementations of the usual chiral and the mixed gauge-gravitational anomalies in four dimensional field theories with chiral fermions. We discuss the holographic renormalization and show that the gauge-gravitational Chern-Simons term does not induce new divergences. In order to cancel contributions from the extrinsic curvature at a boundary at finite distance a new type of counterterm has to be added however. This counterterm can also serve to make the Dirichlet problem well defined in case the gauge field strength vanishes on the boundary. A charged asymptotically AdS black hole is a solution to the theory and as an application we compute the chiral magnetic and chiral vortical conductivities via Kubo formulas. We find that the characteristic term proportional to T2 is present also at strong coupling and that its numerical value is not renormalized compared to the weak coupling result.

Holographic gravitational anomaly and chiral vortical effect

The essence of the chiral magnetic effect is generation of an electric current along an external magnetic field. Recently it has been studied by Rebhan, Schmitt, and Stricker within the Sakai-Sugimoto model, where it was shown to be zero. As an alternative, we calculate the chiral magnetic effect in soft-wall AdS/QCD and find a nonzero result with the natural boundary conditions. The mechanism of the dynamical neutralization of the chiral chemical potential via the string production is discussed in the dual two-form representation.

Chiral magnetic effect in the soft-wall AdS/QCD model

In this paper we discuss a few issues concerning the magnetic susceptibility of the quark condensate and the Son-Yamamoto anomaly matching equation. It is shown that the Son-Yamamoto relation in the IR implies a nontrivial interplay between the kinetic and Wess-Zumino-Witten terms in the chiral Lagrangian. It is also demonstrated that in a holographic framework an external magnetic field triggers mixing between scalar and tensor fields. Accounting for this, one may calculate the magnetic susceptibility of the quark condensate to all orders in the magnetic field.

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More on the Tensor Response of the QCD Vacuum to an External Magnetic Field

https://doi.org/10.1016/j.neuropsychologia.2023.108583

P. N. Kopnin

Papers

Chiral magnetic effect in the soft-wall AdS/QCD model

More on the Tensor Response of the QCD Vacuum to an External Magnetic Field

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