Topological charge changing transitions can induce chirality in the quark-gluon plasma by the axial anomaly. We study the equilibrium response of the quark-gluon plasma in such a situation to an external magnetic field. To mimic the effect of the topological charge changing transitions we will introduce a chiral chemical potential. We will show that an electromagnetic current is generated along the magnetic field. This is the chiral magnetic effect. We compute the magnitude of this current as a function of magnetic field, chirality, temperature, and baryon chemical potential.

Chiral magnetic effect

Matter at high density and low temperature is expected to be a color superconductor, which is a degenerate Fermi gas of quarks with a condensate of Cooper pairs near the Fermi surface that induces color Meissner effects. At the highest densities, where the QCD coupling is weak, rigorous calculations are possible, and the ground state is a particularly symmetric state, the color-flavor locked (CFL) phase. The CFL phase is a superfluid, an electromagnetic insulator, and breaks chiral symmetry. The effective theory of the low-energy excitations in the CFL phase is known and can be used, even at more moderate densities, to describe its physical properties. At lower densities the CFL phase may be disfavored by stresses that seek to separate the Fermi surfaces of the different flavors, and comparison with the competing alternative phases, which may break translation and/or rotation invariance, is done using phenomenological models. We review the calculations that underlie these results and then discuss transport properties of several color-superconducting phases and their consequences for signatures of color superconductivity in neutron stars.

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Color superconductivity in dense quark matter

Weyl points can be thought of as magnetic monopoles in momentum space that always appear in pairs. Magnetoresistance measurements indicate the existence of the long-anticipated chiral anomaly in Weyl semimetal TaAs single crystals.

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Observation of the Chiral-Anomaly-Induced Negative Magnetoresistance in 3D Weyl Semimetal TaAs

Magnetic fields created in the noncentral heavy-ion collision are studied within a microscopic transport model, namely the Ultrarelativistic Quantum Molecular Dynamics model (UrQMD). Simulations were carried out for different impact parameters within the SPS energy range (Elab = 10-158A GeV) and for highest energies accessible for RHIC. We show that the magnetic field emerging in heavy-ion collisions has the magnitude of the order of $eB_y \sim 10^{-1} \cdot m_\pi^2$ for the SPS energy range and $eB_y \sim m_\pi^2$ for the RHIC energies. The estimated value of the magnetic field strength for the LHC energy amounts to $eB_y\sim 15 \cdot m_\pi^2$.

Estimate of the magnetic field strength in heavy-ion collisions

We provide a broad overview of the theoretical status and phenomenological applications of the Color Glass Condensate effective field theory describing universal properties of saturated gluons in hadron wavefunctions that are extracted from deeply inelastic scattering and hadron-hadron collision experiments at high energies.

The Color Glass Condensate

The effects of topological charge change in heavy ion collisions: “Event by event P and CP violation”

Gluon field configurations with nonzero topological charge generate chirality, inducing P- and CP-odd effects. When a magnetic field is applied to a system with nonzero chirality, an electromagnetic current is generated along the direction of the magnetic field. The induced current is equal to the chiral magnetic conductivity times the magnetic field. In this article we will compute the chiral magnetic conductivity of a high-temperature plasma for nonzero frequencies. This allows us to discuss the effects of time-dependent magnetic fields, such as produced in heavy ion collisions, on chirally asymmetric systems.

Chiral Magnetic conductivity

In quantum chromodynamics, a gauge field configuration with nonzero topological charge generates a difference between the number of left- and right-handed quarks. When a (electromagnetic) magnetic field is added to this configuration, an electromagnetic current is induced along the magnetic field; this is called the chiral magnetic effect. We compute this current in the presence of a color-flux tube possessing topological charge, with a magnetic field applied perpendicular to it. We argue that this situation is realized at the early stage of relativistic heavy-ion collisions.

Real-time dynamics of the chiral magnetic effect.

We investigate the effect of a magnetic field on cold dense quark matter using an effective model with four-Fermi interactions. We find that the gap parameters representing the predominant pairing between the different quark flavors show oscillatory behavior as a function of the magnetic field. We point out that due to electric and color neutrality constraints the magnetic fields as strong as presumably existing inside magnetars might induce significant deviations from the gap structure at a zero magnetic field.

Harmen J. Warringa

Papers

Chiral magnetic effect

The effects of topological charge change in heavy ion collisions: “Event by event P and CP violation”

Chiral Magnetic conductivity

Real-time dynamics of the chiral magnetic effect.

Color Superconducting Matter in a Magnetic Field