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.

Quantum chromodynamics (QCD) contains field configurations which can be characterized by a topological invariant, the winding number Q w . Configurations with nonzero Q w break the charge-parity (CP) symmetry of QCD. We consider a novel mechanism by which these configurations can separate charge in the presence of a background magnetic field -the "Chiral Magnetic Effect". We argue that sufficiently large magnetic fields are created in heavy ion collisions so that the Chiral Magnetic Effect causes preferential emission of charged particles along the direction of angular momentum. Since separation of charge is CP-odd, any observation of the Chiral Magnetic Effect could provide a clear demonstration of the topological nature of the QCD vacuum. We give an estimate of the effect and conclude that it might be observed experimentally.

Gluon field configurations with nonzero topological charge generate chirality, inducing P-and CPodd 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.

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.Introduction. The theory of the strong interactions, quantum chromodynamics (QCD), is an SU(3) YangMills theory coupled to fermions (quarks). An intriguing aspect of SU(N ) Yang-Mills theories is their relation to topology. This reveals itself in the existence of gauge field configurations carrying topological charge Q [1]. This charge is quantized as an integer if these configurations interpolate between two of the infinite number of degenerate vacua of the SU(N ) Yang-Mills theory [2]. Expressed in terms of the field strength tensor G

We investigate the effect of a magnetic field on cold dense three-flavor quark matter using an effective model with four-Fermi interactions with electric and color neutrality taken into account. The gap parameters ∆1, ∆2, and ∆3 representing respectively the predominant pairing between down and strange (d-s) quarks, strange and up (s-u) quarks, and up and down (u-d) quarks, show the de Haas-van Alphen effect, i.e. oscillatory behavior as a function of the modified magnetic fieldB that can penetrate the color superconducting medium. Without applying electric and color neutrality we find ∆2 ≃ ∆3 ≫ ∆1 for 2ẽB > µ 2 q , whereẽ is the modified electromagnetic coupling constant and µq is one third of the baryon chemical potential. Because the average Fermi surface for each pairing is affected by taking into account neutrality, the gap structure changes drastically in this case; we find ∆1 ≫ ∆2 ≃ ∆3 for 2ẽB > µ 2 q . We point out that the magnetic fields as strong as presumably existing inside magnetars might induce significant deviations from the gap structure ∆1 ≃ ∆2 ≃ ∆3 at zero magnetic field.PACS numbers: 12.38. Aw, 24.85.+p, 26.60.+c By analyzing Quantum Chromodynamics (QCD) it has been established that at zero temperature and high enough baryon densities color superconducting (CSC) matter should be formed [1]. Unfortunately no experimental evidence for color superconductivity is yet available. In CSC matter Cooper pairs of quarks are created due to an attractive interaction between quarks on opposite sides of the Fermi surface. The (almost) sole place where one might be able to find color superconductivity in nature would be the central part of neutron stars. To this aim one has to clarify the properties of CSC matter under the physical conditions maintained inside neutron stars [2,3].The neutron star density is at most ρ ∼ 10ρ 0 in the core, where ρ 0 is the normal nuclear density ∼ 0.17 nucleon/fm 3 . This density roughly corresponds to a quark chemical potential (i.e. one third of the baryon chemical potential) µ q ∼ 500 MeV as deduced from ρ ∼ 3µ 3 q /π 2 . At this intermediate density one cannot neglect the role of the strange quark mass M s = 100 ∼ 200 MeV. The strange quark mass induces a "pressure" to tear the Cooper pairs apart, i.e., a Fermi surface mismatch of size M 2 s /2µ q between u/d quarks and s quarks will be formed. The pairing pattern is quite complicated in the density region where M 2 s /2µ q is comparable to the gap energy ∆ which are both of order tens MeV around the region of our interest where µ q ∼ 500 MeV.The Fermi surface mismatch is further caused by the requirement of neutrality which is broken by M s = 0 in three-flavor quark matter. The system should be electric neutral to avoid divergent field energies faster than the volume, otherwise the system is not stable thermodynamically. Regarding color neutrality the constraint is more stringent, that is, the whole system must be a color-singlet. To consider the phase structure, however, it is adequate to impose global color neutrali...