The interplay of quantum anomalies with magnetic field and vorticity results in a variety of novel non-dissipative transport phenomena in systems with chiral fermions, including the quarkgluon plasma. Among them is the Chiral Magnetic Effect (CME) -the generation of electric current along an external magnetic field induced by chirality imbalance. 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 strongly coupled quark-gluon plasma, and can be studied in relativistic heavy ion collisions where strong magnetic fields are created by the colliding ions. Evidence for the CME and related phenomena has been reported by the STAR Collaboration at Relativistic Heavy Ion Collider at BNL, and by the ALICE Collaboration at the Large Hadron Collider at CERN. The goal of the present review is to provide an elementary introduction into the physics of anomalous chiral effects, to describe the current status of experimental studies in heavy ion physics, and to outline the future work, both in experiment and theory, needed to eliminate the existing uncertainties in the interpretation of the data. Superconductors also demonstrate the deep link between topology and non-dissipative currents.Since this link is of crucial importance for our discussion, let us elaborate on it by using superconductor as an example. Around the Abrikosov vortex, there exists a supercurrent that screens the magnetic field of the vortex in the bulk. The corresponding physics is captured by the London relation between the electric current and gauge potential (∇ · A = 0):(1)

A number of theoretical and lattice results lead us to believe that Quark-Gluon Plasma not too far from Tc contains not only electrically charged quasiparticles -quarks and gluons -but magnetically charged ones -monopoles and dyons -as well. Although binary systems like charge-monopole and charge-dyon were considered in details before in both classical and quantum settings, it is the first study of coexisting electric and magnetic particles in many-body context. We perform Molecular Dynamics study of strongly coupled plasmas with ∼ 1000 particles and different fraction of magnetic charges. Correlation functions and Kubo formulae lead to such transport properties as diffusion constant, shear viscosity and electric conductivity: we compare the first two with empirical data from RHIC experiments as well as results from AdS/CFT correspondence. We also study a number of collective excitations in these systems.

The chiral magnetic wave is a gapless collective excitation of quark-gluon plasma in the presence of an external magnetic field that stems from the interplay of chiral magnetic and chiral separation effects; it is composed of the waves of the electric and chiral charge densities coupled by the axial anomaly. We consider a chiral magnetic wave at finite baryon density and find that it induces the electric quadrupole moment of the quark-gluon plasma produced in heavy ion collisions: the "poles" of the produced fireball (pointing outside of the reaction plane) acquire additional positive electric charge, and the "equator" acquires additional negative charge. We point out that this electric quadrupole deformation lifts the degeneracy between the elliptic flows of positive and negative pions leading to v(2)(π(+))

We review the present status of the search for a phase transition and critical point as well as anomalous transport phenomena in Quantum Chromodynamics (QCD), with an emphasis on the Beam Energy Scan program at the Relativistic Heavy Ion Collider at Brookhaven National Laboratory. We present the conceptual framework and discuss the observables deemed most sensitive to a phase transition, QCD critical point, and anomalous transport, focusing on fluctuation and correlation measurements. Selected experimental results for these observables together with those characterizing the global properties of the systems created in heavy ion collisions are presented. We then discuss what can be already learned from the currently available data about the QCD critical point and anomalous transport as well as what additional measurements and theoretical developments are needed in order to discover these phenomena.

In ultra-relativistic heavy ion collisions, the matter formed shortly after the collision is a dense, out of equilibrium, system of gluons characterized by a semi-hard momentum scale Qs. Simple power counting arguments indicate that this system is over-occupied: the gluon occupation number is parametrically large when compared to a system in thermal equilibrium with the same energy density. On short time scales, soft elastic scatterings tend to drive the system towards the formation of a Bose-Einstein condensate that contains a large fraction of the gluons while contributing little to the energy density. The lifetime and existence of this condensate depends on whether inelastic processes, that occur on the same time scale as the elastic ones, preferably increase or decrease the number of gluons. During this overpopulated stage, and all the way to thermalization, the system behaves as a strongly interacting fluid, even though the elementary coupling constant is small. We argue that while complete isotropization may never be reached, the system may yet evolve for a long time with a fixed anisotropy between average longitudinal and transverse momenta.

The heavy-ion collisions can produce extremely strong transient magnetic and electric fields. We study the azimuthal fluctuation of these fields and their correlations with the also fluctuating matter geometry (characterized by the participant plane harmonics) using event-by-event simulations. A sizable suppression of the angular correlations between the magnetic field and the 2nd and 4th harmonic participant planes is found in very central and very peripheral collisions, while the magnitudes of these correlations peak around impact parameter b ∼ 8 − 10fm for RHIC collisions. This can lead to notable impacts on a number of observables related to various magnetic field induced effects, and our finding suggests that the optimal event class for measuring them should be that corresponding to b ∼ 8 − 10 fm.

The phases and properties of matter under global rotation have attracted much interest recently. In this paper we investigate the pairing phenomena in a system of fermions under the presence of rotation. We find that there is a generic suppression effect on pairing states with zero angular momentum. We demonstrate this effect with the chiral condensation and the color superconductivity in hot dense QCD matter as explicit examples. In the case of chiral condensation, a new phase diagram in the temperature-rotation parameter space is found, with a nontrivial critical point.Introduction.-The phases and properties of matter can become highly nontrivial under rotation, and have attracted a lot of interest recently. Such studies bear particular relevance for the strongly interacting matter of Quantum Chromodynamics (QCD). For example, astrophysical objects like neutron stars, made of dense QCD matter, can be rapidly spinning [1,2]. In relativistic heavy ion collision experiments, the typical collision events are off-central and the created QCD matter will carry a nonzero angular momentum on the order of 10 4 ∼ 10 5 with local angular velocity in the range 0.01 ∼ 0.1GeV [3][4][5][6][7][8]. There has also been impressive progress to study the rotating QCD matter using lattice gauge theory simulations [9].In rotating matter, many interesting transport phenomena could occur. For example, fluid rotation can induce anomalous transport processes in a system of chiral fermions, such as the chiral vortical effect [10][11][12] and chiral vortical wave [13]. These can lead to measurable experimental signals (see e.g. reviews in [14,15]). In such anomalous transport, it is found that the fluid rotation plays a very analogous role to a magnetic field. Indeed there appears to be interesting similarity between the chiral vortical effect and the chiral magnetic effect [10,16], as well as between the chiral vortical wave and the chiral magnetic wave [17,18].Apart from transport properties, it is of significant interest to explore the effects of rotation on the phase transitions of matter in both relativistic and non-relativistic cases. It is well known that a magnetic field can bring interesting effects on the thermodynamics and phase diagram of e.g. QCD matter [19][20][21][22][23][24], such as the magnetic catalysis and inverse catalysis (see reviews in [25,26]) on the chiral condensation. Given the close analogy between rotation and magnetic field, it is tempting to ask how the rotation could influence phase transitions. In this paper, we investigate the pairing phenomena in a system of fermions under rotation. We find a generic suppression effect on pairing states with zero angular momentum,

Recently, there has been significant interest in understanding the macroscopic quantum transport in a many-body system of chiral fermions. A natural framework for describing such a system that is generally out of equilibrium is the transport equation for its phase space distribution function. In this paper, we obtain a complete solution of the covariant chiral transport for massless fermions, by starting from the general Wigner function formalism and carrying out a complete and consistent semiclassical expansion up toÔðℏÞ order. In particular, we clarify certain subtle and confusing issues surrounding the Lorentz noninvariance and frame dependence associated with the three-dimensional chiral kinetic theory. We prove that such frame dependence is uniquely and completely fixed by an unambiguous definition of theÔðℏÞ correction to the distribution function in each reference frame.