Chiral Vortical Effect Research Articles

Covariant chiral kinetic equation in non-Abelian gauge field from \u201ccovariant gradient expansion\u201d

We derive the chiral kinetic equation in 8 dimensional phase space in non- Abelian SU(N) gauge field within the Wigner function formalism. By using the “covariant gradient expansion”, we disentangle the Wigner equations in four-vector space up to the first order and find that only the time-like component of the chiral Wigner function is independent while other components can be explicit derivative. After further decomposing the Wigner function or equations in color space, we present the non-Abelian covariant chiral kinetic equation for the color singlet and multiplet phase-space distribution functions. These phase-space distribution functions have non-trivial Lorentz transformation rules when we define them in different reference frames. The chiral anomaly from non-Abelian gauge field arises naturally from the Berry monopole in Euclidian momentum space in the vacuum or Dirac sea contribution. The anomalous currents as non-Abelian counterparts of chiral magnetic effect and chiral vortical effect have also been derived from the non-Abelian chiral kinetic equation.

Effects of nonhelical component of hypermagnetic field on the evolution of the matter-antimatter asymmetry, vorticity, and hypermagnetic field

We study the evolution of the matter-antimatter asymmetry ({\eta}), the vorticity, and the hypermagnetic field in the symmetric phase of the early Universe, and in the temperature range 100 GeV < T < 10 TeV. We assume a configuration for the hypermagnetic field which includes both helical and non-helical (Bz) components. Consequently, the hypermagnetic field and the fluid vorticity can directly affect each other, the manifestations of which we explore in three scenarios. In the first scenario, we show that in the presence of a small vorticity and a large {\eta}eR, helicity can be generated and amplified for an initially strong Bz. The generation of the helical seed is due to the chiral vortical effect (CVE) and/or the advection term, while its growth is mainly due to the chiral magnetic effect (CME) which leads to the production of the baryon asymmetry, as well. The vorticity saturates to a nonzero value which depends on Bz, even in the presence of the viscosity, due to the back-reaction of Bz on the plasma. Increasing the initial vorticity, makes the values of the helicity, {\eta}s, and vorticity reach their saturation curves sooner, but does not change their final values at the onset of the electroweak phase transition. The second scenario is similar to the first except we assume that all initial {\eta}s are zero. We find that much higher initial vorticity is required for the generation process. In the third scenario, we show that in the presence of only a strong hypermagnetic field, {\eta}s and vorticity can be generated and amplified. Increasing the initial helicity, increases the final {\eta}s and vorticity. We find that although the presence of a nonzero initial Bz is necessary in all three scenarios, its increase only increases the final values of vorticity.

Born-Infeld generalization: Axion and Kalb-Ramond from dynamical torsion fields

We show that in theories of gravitation based on affine geometries the torsion field, that takes a dynamical character, not only the chiral magnetic effect (CME) intervenes in the wash up of the chiral anomaly but also the chiral vortical effect (CVE) and the coupled chiral effect (CCE) coming from the hypermagnetic field interaction with the primordial plasma are crucial in a realistic physical scenario, as in the case of the early universe. We also show that the equation governing the wash up takes the form given in this paper, supplemented with the dynamical equation for the torsion vector containing the helicities and other axial couplings. The role played by the neutrinos in the interaction with the axion field in this theoretical framework is briefly discussed.

Chiral transport in curved spacetime via holography

We consider a holographic model of strongly interacting plasma with a gravitational anomaly. In this model, we compute parity-odd responses of the system at finite temperature and chemical potential to external electromagnetic and gravitational fields. Working within the linearized fluid/gravity duality, we performed the calculation up to the third order in gradient expansion. Besides reproducing the chiral magnetic (CME) and vortical (CVE) effects we also obtain gradient corrections to the CME and CVE due to the gravitational anomaly. Additionally, we find energy-momentum and current responses to the gravitational field similarly determined by the gravitational anomaly. The energy-momentum response is the first purely gravitational transport effect that has been related to quantum anomalies in a holographic theory.

Chiral effects on rotating and accelerated backgrounds

If the gauge quantum chiral anomaly predicts chiral effects related to chemical potentials, then the gravitational chiral anomaly is responsible for the effects of temperature. The prediction of the gravitational anomaly for the temperature term in the chiral vortical effect coincides with the prediction of statistical calculations by the Kubo formula for spin 1/2, but two predictions disagree already for spin 1. A solution to this problem related to the features of infrared regularization is described. Also the thermodynamic instability in systems with acceleration, which occurs at temperatures below the Unruh temperature and the transition through the Unruh temperature are discussed.

On chiral responses to geometric torsion

We show that geometric torsion does not lead to new chiral dissipationless transport effects. Instead apparent response to torsion can be viewed as a manifestation of the chiral vortical effect.

The generation of matter\u2013antimatter asymmetries and hypermagnetic fields by the chiral vortical effect of transient fluctuations

We study the contribution of the temperature-dependent chiral vortical effect to the generation and evolution of hypermagnetic fields and matter-antimatter asymmetries, in the symmetric phase of the early Universe, in the temperature range 100 GeV le T le 10 TeV. Our most important result is that, due to the chiral vortical effect, small overlapping transient fluctuations in the vorticity field in the plasma and temperature of matter degrees of freedom can lead to the generation of strong hypermagnetic fields and matter-antimatter asymmetries, all starting from zero initial values. We show that, either an increase in the amplitudes of the fluctuations of vorticity or temperature, or a decrease in their widths, leads to the production of stronger hypermagnetic fields, and therefore, larger matter-antimatter asymmetries. We have the interesting result that fluctuating vorticity fields are more productive, by many orders of magnitude, as compared to vorticities that are constant in time.

Magneto-vortical effect in strong magnetic field

We develop covariant chiral kinetic theory with Landau level basis. We use it to investigate a magnetized plasma with a transverse electric field and a steady vorticity as perturbations. After taking into account vacuum shift in the latter case, we find the resulting current and stress tensor in both cases can be matched consistently with constitutive equations of magnetohydrodynamics. We find the solution in the vorticity case contains both shifts in temperature and chemical potential as well as excitations of the lowest Landau level states. The solution gives rise to an vector charge density and axial current density. The vacuum parts coming from both shifts and excitations agree with previous studies and the medium parts coming entirely from excitations leads to a new contribution to vector charge and axial current density consistent with standard chiral vortical effect.

From chiral kinetic theory to relativistic viscous spin hydrodynamics

In this work, we start with chiral kinetic theory and construct the spin hydrodynamic framework for a chiral spinor system. Using the 14-moment expansion formalism, we obtain the equations of motion of second-order dissipative relativistic fluid dynamics with non-trivial spin polarization density. In a chiral spinor system, the spin alignment effect could be treated in the same framework as the Chiral Vortical Effect (CVE). However, the quantum corrections due to fluid vorticity induce not only CVE terms in the vector/axial charge currents but also corrections to the stress tensor. In this framework, viscous corrections to the hadron spin polarization are self-consistently obtained, which will be important for the precise prediction of the polarization rate for the observed hadrons, e.g. $\Lambda$-hyperon.

Chiral vortical effect for vector fields

We consider the photonic vortical effect, i.e., the difference of the flows of left- and right-handed photons along the vector of angular velocity in rotating photonic medium. Two alternative frameworks to evaluate the effect are considered, both of which have already been tried in the literature: first, the standard thermal field theory and, alternatively, Hawking-radiation-type derivation. In our earlier attempt to compare the two approaches, we found a crucial factor of 2 difference. Here, we revisit the problem, paying more attention to details of infrared regularizations. We find out that introduction of an infinitesimal mass of the vector field brings the two ways of evaluating the chiral vortical effect into agreement with each other. Some implications, on both the theoretical and phenomenological sides, are mentioned.

Macroscopic Manifestations of Quantum Anomalies in Hydrodynamics (Brief Review)

We present a mini-review of (some aspects of the) theory of so called chiral effects in hydrodynamic approximation. One considers fluids whose constituents are massless fermions. The underlying field theory incorporates quantum anomalies which are loop effects in gauge-field backgrounds not consistent with the chiral symmetry of the classical lagrangian. One of central theoretical claims is that the quantum anomalies trigger macroscopic fluid motions of calculable amplitude. An example is provided by the chiral vortical effect which is a helical motion of the fluid transporting the chiral charge along the axis of a vortex.

Wigner functions and quantum kinetic theory of polarized photons

We derive the Wigner functions of polarized photons in the Coulomb gauge with the ħ expansion applied to quantum field theory, and identify side-jump effects for massless photons. We also discuss the photonic chiral vortical effect for the Chern-Simons current and zilch vortical effect for the zilch current in local thermal equilibrium as a consistency check for our formalism. The results are found to be in agreement with those obtained from different approaches. Moreover, using the real-time formalism, we construct the quantum kinetic theory (QKT) for polarized photons. By further adopting a specific power counting scheme for the distribution functions, we provide a more succinct form of an effective QKT. This photonic QKT involves quantum corrections associated with self-energy gradients in the collision term, which are analogous to the side-jump corrections pertinent to spin-orbit interactions in the chiral kinetic theory for massless fermions. The same theoretical framework can also be directly applied to weakly coupled gluons in the absence of background color fields.

Quantum kinetic theory for spin-1/2 fermions in Wigner function formalism

We give a brief overview of the kinetic theory for spin-1/2 fermions in Wigner function formalism. The chiral and spin kinetic equations can be derived from equations for Wigner functions. A general Wigner function has 16 components which satisfy 32 coupled equations. For massless fermions, the number of independent equations can be significantly reduced due to the decoupling of left-handed and right-handed particles. It can be proved that out of many components of Wigner functions and their coupled equations, only one kinetic equation for the distribution function is independent. This is called the disentanglement theorem for Wigner functions of chiral fermions. For massive fermions, it turns out that one particle distribution function and three spin distribution functions are independent and satisfy four kinetic equations. Various chiral and spin effects such as chiral magnetic and vortical effects, the chiral separation effect, spin polarization effects can be consistently described in the formalism.

Local spin polarizations in relativistic heavy-ion collisions

Based on a generalized side-jump formalism for massless chiral fermions, which naturally takes into account the spin-orbit coupling in the scattering of two chiral fermions and the chiral vortical effect in a rotating chiral fermion matter, we have developed a covariant and total-angular-momentum-conserved chiral transport model to study both the global and local polarizations of this matter. For a system of massless quarks of random spin orientations and finite vorticity in a box, we have demonstrated that the model can exactly conserve the total angular momentum of the system and dynamically generate the quark spin polarization expected from a thermally equilibrated quark matter. Using this model to study the spin polarization in relativistic heavy-ion collision, we have found that the local quark spin polarizations depend strongly on the reference frame where they are evaluated as a result of the nontrivial axial charge distribution caused by the chiral vortical effect. We have further shown that because of the anomalous orbital or side-jump contribution to the quark spin polarization, the local quark polarizations calculated in the medium rest frame are qualitatively consistent with the local polarizations of Lambda hyperons measured in experiments.

Vorticity and Spin Polarization — A Theoretical Perspective

We give a theoretical perspective on the vorticity and spin polarization in heavy-ion collisions. We discuss the recent progress in spin hydrodynamics and spin kinetic theory. We also discuss other effects caused by vorticity including the chiral vortical effect and rotation-induced phase transitions.

Chiral vortical effect: Black-hole versus flat-space derivation

The chiral vortical effect (CVE) was derived first for non-interacting massless fermions. Recently, an alternative derivation of the CVE was suggested which relates it to the radiation from the horizon of a rotating black hole. We attempt to generalize the latter derivation to the case of photons and encounter a crucial factor of two difference between the two ways of visualizing the CVE. Reservations and possible explanations are briefly discussed.

Out of equilibrium chiral vortical effect in holography

We study the chiral vortical effect far from equilibrium in a strongly coupled holographic field theory. Rotation is represented as a perturbation via a gravito-magnetic field on top of a five-dimensional charged AdS Vaidya metric. We also introduce a momentum relaxation mechanism by linear scalar field backgrounds and study the CVE dynamics as function of the charges, temperature and momentum relaxation. The far from equilibrium behavior shows that the CVE builds up with a significant delay in time compared to the quasi instantaneous equilibration of the background metric. We also pay special attention to the effects of the gravitational contribution to the axial anomaly in the CVE of the axial current. We develop an analytic estimate of this delay and also compute the quasi-normal modes near equilibrium which determine the late time ring down.

Chiral vortical effect in relativistic and nonrelativistic systems

We formulate the chiral vortical effect (CVE) and its generalization called generalized vortical effect using the semiclassical theory of wave packet dynamics. We take the spin-vorticity coupling into account and calculate the transport charge current by subtracting the magnetization one from the Noether local one. We find that the transport charge current in the CVE always vanishes in relativistic chiral fermions. This result implies that it cannot be observed in transport experiments in condensed matter systems such as Dirac/Weyl semimetals with the pseudo-Lorentz symmetry. We also demonstrate that the anisotropic CVE can be observed in nonrelativistic systems that belong to the point groups $D_n, C_n (n = 2, 3, 4, 6)$, and $C_1$, such as $n$-type tellurium.

Mode decomposed chiral magnetic effect and rotating fermions

We present a novel perspective to characterize the chiral magnetic and related effects in terms of angular decomposed modes. We find that the vector current and the chirality density are connected through a surprisingly simple relation for all the modes and any mass, which defines the mode decomposed chiral magnetic effect in such a way free from the chiral chemical potential. The mode decomposed formulation is useful also to investigate properties of rotating fermions. For demonstration, we give an intuitive account for a nonzero density emerging from a combination of rotation and magnetic field as well as an approach to the chiral vortical effect at finite density.

Acceleration and rotation in quantum statistical theory

The derivation of fundamental effects related to the rotation and acceleration of a medium consisting of relativistic particles based on quantum-statistical approaches is presented. The Unruh effect for an accelerated medium is derived based on the Zubarev density operator. A nonperturbative formula is obtained for the chiral vortical effect (CVE) in a medium with vorticity at a finite mass based on a generalization of the first terms of the quantum-field perturbation theory calculated using the statistical operator. Various corrections to these effects in higher orders in acceleration and vorticity were found. The concept of vorticity and acceleration as new real and imaginary chemical potentials is substantiated. The duality of the quantum-statistical Zubarev density operator and quantum field theory in a space-time with a conical singularity is revealed and shown by the example of the correspondence of quantum corrections with acceleration in two approaches. The consequences of this duality for both methods are investigated. A new effect related to thermodynamic instability at the Unruh temperature is shown.