We derive the chiral kinetic theory under the presence of a gravitational Riemann curvature. It is well-known that in the chiral kinetic theory there inevitably appears a redundant ambiguous vector corresponding to the choice of the Lorentz frame. We reveal that on top of this conventional frame choosing vector, higher-order quantum correction to the chiral kinetic theory brings an additional degrees of freedom to specify the distribution function. Based on this framework, we derive new types of fermionic transport, that is, the charge current and energy-momentum tensor induced by the gravitational Riemann curvature. Such novel phenomena arise not only under genuine gravity but also in a (pseudo-)relativistic fluid, for which inhomogeneous vorticity or temperature are effectively represented by spacetime metric tensor. It is especially found that the charge and energy currents are antiparallelly induced by an inhomogeneous fluid vorticity (more generally, by the Ricci tensor ${R_0}^i$), as a consequence of the spin-curvature coupling. We also briefly discuss possible applications to Weyl/Dirac semimetals and heavy-ion collision experiments.
We study collective excitations in hot rotating chiral media in presence of magnetic field in kinetic theory, namely Chiral Heat Wave and its' mixings with Chiral Vortical Wave and Chiral Magnetic Wave. Our results for velocities of these waves have slight alterations from those obtained earlier. We explain the origin of these alterations and also give the most general expressions for the velocities of all these waves in hydrodynamic approach.
The consistent chiral kinetic theory accurate to the second order in electromagnetic and pseudoelectromagnetic fields is derived for a relativistic matter with two Weyl fermions. By making use of such a framework, the properties of longitudinal collective excitations, which include both chiral magnetic and chiral pseudomagnetic waves, are studied. It is shown that the proper treatment of dynamical electromagnetism transforms these gapless waves into chiral (pseudo)magnetic plasmons, whose Langmuir (plasma) gap receives corrections quadratic in both magnetic and pseudomagnetic fields.
A modified quantum kinetic equation which takes account of the noninertial features of rotating frame is proposed. The vector and axial-vector field components of the Wigner function for chiral fluids are worked out in a semiclassical scheme. It is demonstrated that the chiral currents and energy-momentum tensor computed by means of them are consistent with the hydrodynamical results. A new semiclassical covariant chiral transport equation is established by inspecting the equations satisfied by the chiral vector fields. It uniquely provides a new three-dimensional semiclassical chiral kinetic …
We derive the non-equilibrium kinetic equation describing the motion of chiral massless particles in the regime where it can be considered classically. We show that the Berry monopole which appears at the origin of the momentum space due to level crossing is responsible for the chiral magnetic and vortical effects.
We revisit the chiral anomaly in the quantum kinetic theory in the Wigner function formalism under the background field approximation. Our results show that the chiral anomaly is actually from the Dirac sea or the vacuum contribution in the un-normal-ordered Wigner function. We also demonstrate that this contribution modifies the chiral kinetic equation for antiparticles.
Many-body systems with chiral fermions exhibit anomalous transport phenomena originated from quantum anomalies. Based on quantum field theory, we derive the kinetic theory for chiral fermions interacting with an external electromagnetic field and a background curved geometry. The resultant framework respects the covariance under the U(1) gauge, local Lorentz, and diffeomorphic transformations. It is particularly useful to study the gravitational or non-inertial effects for chiral systems. As the first application, we study the chiral dynamics in a rotating coordinate and clarify the roles of t…
We study fermion mass correction to chiral kinetic equations in electromagnetic fields. Different from the chiral limit where fermion number density is the only independent distribution, the number and spin densities are coupled to each other for massive fermion systems. To the first order in $\hbar$, we derived the quantum correction to the classical on-shell condition and the Boltzmann-type transport equations. To the linear order in the fermion mass, the mass correction does not change the structure of the chiral kinetic equations and behaves like additional collision terms. While the mass …
We study fermion mass correction to chiral kinetic equations in electromagnetic fields. Different from the chiral limit where fermion number density is the only independent distribution, the number and spin densities are coupled to each other for massive fermion systems. To the first order in $\hbar$, we derived the quantum correction to the classical on-shell condition and the Boltzmann-type transport equations. To the linear order in the fermion mass, the mass correction does not change the structure of the chiral kinetic equations and behaves like additional collision terms. While the mass …
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 …
We study the two-point functions from chiral kinetic theory which characterize the response to perturbative vector and axial gauge fields in magnetized chiral plasma. In the lowest Landau level approximation, the solution of chiral kinetic equations gives density waves of electric and axial charges, which contain chiral magnetic wave implied by the axial anomaly and magnetic field. We then obtain the constitutive relations for covariant currents and stress tensor that involving the density waves. By considering the difference between consistent and covariant anomalies explicitly, the correlato…
Using a covariant formalism, we construct a chiral kinetic theory Lorentz invariant to order $\mathcal O(\hbar)$ which includes collisions. We find a new contribution to the particle number current due to the side jumps required by the conservation of angular momentum during collisions. We also find a conserved symmetric stress-energy tensor as well as the $H$-function obeying Boltzmann's $H$-theorem. We demonstrate their use by finding a general equilibrium solution and the values of the anomalous transport coefficients characterizing chiral vortical effect.
By using the exact solutions of the Weyl equation in a constant magnetic field, the equal-time Wigner function for magnetized chiral plasma is derived. It is found that the dependence of the Wigner function on the component of momentum along the magnetic field is asymmetric and is correlated with the fermion chirality. Such a dependence is principal for reproducing the correct chiral magnetic and chiral separation effects. In the lowest Landau level approximation, the equation for the equal-time Wigner function in a strong magnetic field is derived. By making use of this equation, it is found …
We study collective excitations in systems described by chiral kinetic theory in external magnetic field. We consider high-temperature weak-coupling plasma, as well as high-density Landau Fermi liquid with interaction not restricted to be weak. We show that chiral magnetic wave (CMW) emerges in hydrodynamic regime (at frequencies smaller than collision relaxation rate) and the CMW velocity is determined by thermodynamic properties only. We find that in a plasma of opposite chiralities, at frequencies smaller than the chirality-flipping rate, the CMW excitation turns into a vector-like diffusio…
We outline a novel chiral kinetic theory framework for systematic computations of the Chiral Magnetic Effect (CME) in ultrarelativistic heavy-ion collisions. The real part of the fermion determinant in the QCD effective action is expressed as a supersymmetric world-line action of spinning, colored, Grassmanian point particles in background gauge fields, with equations of motion that are covariant generalizations of the Bargmann-Michel-Telegdi and Wong equations. Berry's phase is obtained in a consistent non-relativistic adiabatic limit. The chiral anomaly, in contrast, arises from the phase of…
In heavy-ion collisions, an interesting question of phenomenological relevance is how the chiral imbalance generated at early times persists through a fluctuating background of sphalerons in addition to other "non-anomalous" interactions with the QGP. To address this question, we construct a relativistic chiral kinetic theory using the world-line formulation of quantum field theory. We outline how Berry's phase arises in this framework, and how its effects can be clearly distinguished from those arising from the chiral anomaly. We further outline how this framework can be matched to classical …
By making use of the chiral kinetic theory in the relaxation-time approximation, we derive an Israel-Stewart type formulation of the hydrodynamic equations for a chiral relativistic plasma made of neutral particles (e.g., neutrinos). The effects of chiral asymmetry are captured by including an additional continuity equation for the axial charge, as well as the leading-order quantum corrections due to the spin of particles. In a formulation of the chiral kinetic theory used, we introduce a symmetric form of the energy-momentum tensor that is suitable for the description of a weakly nonuniform c…
Recently there has been significant interest in the macroscopic manifestation of chiral anomaly in many-body systems of chiral fermions. A notable example is the Chiral Magnetic Effect (CME). Enthusiastic efforts have been made to search for the CME in the quark-gluon plasma created in heavy ion collisions. A crucial challenge is that the extremely strong magnetic field in such collisions may last only for a brief moment and the CME current may have to occur at so early a stage that the quark-gluon matter is still far from thermal equilibrium. This thus requires modeling of the CME in an out-o…
The chiral kinetic theory of Weyl fermions with collisions in the presence of weak electric and magnetic fields is derived from quantum field theories. It is found that the side-jump terms in the perturbative solution of Wigner functions play a significant role for the derivation. Moreover, such terms manifest the breaking of Lorentz symmetry for distribution functions. The Lorentz covariance of Wigner functions thus leads to modified Lorentz transformation associated with side-jump phenomena further influenced by background fields and collisions.
We explicitly calculate the one-loop effective potential for a higher-derivative four-dimensional chiral superfield theory with a nonconventional kinetic term. We consider the cases of minimal and nonminimal general Lagrangians. In particular, we find that in the minimal case the divergent part of the one-loop effective potential vanishes by reason of the chirality.
We introduce the quantum-field-theory (QFT) derivation of chiral kinetic theory (CKT) from the Wigner-function approach, which manifests side jumps and non-scalar distribution functions associated with Lorentz covariance and incorporates both background fields and collisions. The formalism is utilized to investigate second-order responses of chiral fluids near local equilibrium. Such non-equilibrium anomalous transport is dissipative and affected by interactions. Contributions from both quantum corrections in anomalous hydrodynamic equations (EOM) of motion and those from the CKT and Wigner fu…
We use the recently developed kinetic theory with Berry curvature to describe the fermions and antifermions of a chiral relativistic plasma. We check that this transport approach allows to reproduce the chiral anomaly equation of relativistic quantum field theory at finite temperature. We also check that it allows to describe the anomalous gauge polarization tensor that appears in the Hard Thermal (and/or Dense) effective field theory. We also construct an energy density associated to the gauge collective modes of the chiral relativistic plasma, valid in the case of small couplings or weak fie…
Extra dimensions have been used as attempts to explain several phenomena in particle physics. In this paper we investigate the role of brane-localized kinetic terms (BLKT) on thin and thick branes with two flat extra dimensions (ED) compactified on the chiral square, and an abelian gauge field in the bulk. The results for a thin brane have resemblance with the 5-D case, leading to a tower of massive KK particles whose masses depend upon the compactification radius and the BLKT parameter. On the other hand, for the thick brane scenario, there is no solution that satisfy the boundary conditions.…
We study the hydrodynamics of a gas of noninteracting Weyl fermions coupled to the electromagnetic field in $(2N + 1) + 1$ spacetime dimensions using the chiral kinetic theory, which encodes the gauge anomaly in the Chern character of the nonabelian Berry connection over the Fermi surface. We derive the anomalous contributions to the relativistic hydrodynamic currents in equilibrium and at a finite temperature, which agree with and provides an approach complementary to the results derived previously using thermodynamic constraints.
We give a brief overview of the kinetic theory for spin-1/2 fermions in Wigner function formulism. 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 call…
We derive a relativistic chiral kinetic equation with manifest Lorentz covariance from Wigner functions of spin-1/2 massless fermions in a constant background electromagnetic field. It contains vorticity terms and a 4-dimensional Euclidean Berry monopole which gives axial anomaly. By integrating out the zero-th component of the 4-momentum p, we reproduce the previous 3-dimensional results derived from the Hamiltonian approach, together with the newly derived vorticity terms. The phase space continuity equation has an anomalous source term proportional to the product of electric and magnetic fi…
We propose a classical action for the motion of massless Weyl fermions in a background gauge field in (2N+1)+1 spacetime dimensions. We use this action to derive the collisionless Boltzmann equation for a gas of such particles, and show how classical versions of the gauge and Abelian chiral anomalies arise from the Chern character of the non-Abelian Berry connection that parallel transports the spin degree of freedom in momentum space.
We argue that the correct definition of the electric current in the chiral kinetic theory for Weyl materials should include the Chern-Simons contribution that makes the theory consistent with the local conservation of the electric charge in electromagnetic and strain-induced pseudoelectromagnetic fields. By making use of such a kinetic theory, we study the plasma frequencies of collective modes in Weyl materials in constant magnetic and pseudomagnetic fields, taking into account the effects of dynamical electromagnetism. We show that the collective modes are chiral plasmons. While the plasma f…
Using the chiral kinetic theory we derive the electric and chiral current densities in inhomogeneous relativistic plasma. We also derive equations for the electric and chiral charge chemical potentials that close the Maxwell equations in such a plasma. The analysis is done in the regimes with and without a drift of the plasma as a whole. In addition to the currents present in the homogeneous plasma (Hall current, chiral magnetic, chiral separation, and chiral electric separation effects, as well as Ohm's current) we derive several new terms associated with inhomogeneities of the plasma. Apart …
Finding signatures of dark matter in transport characteristics of solids would be an important step on the road to detect this illusive component of the mass of our Universe. This is especially important and timely as the experiments designed to directly detect dark matter particles continue to provide negative results. As a first step in this direction we consider topologically non-trivial Weyl or Dirac semimetals and derive the modified kinetic equation taking into account two coupled $U(1)$-gauge fields, one being the standard Maxwell electromagnetic field and other corresponding to the dar…
Semiclassical chiral kinetic theories in the presence of electromagnetic fields as well as vorticity can be constructed by means of some different relativistic or nonrelativistic approaches. To cover the noninertial features of rotating frames one can start from the modified quantum kinetic equation of Wigner function in Minkowski spacetime. It provides a relativistic chiral transport equation whose nonrelativistic limit yields a consistent three-dimensional kinetic theory which does not depend explicitly on spatial coordinates. Recently a chiral transport equation in curved spacetime has been…
We study the effect of a small fermion mass in the formulation of the on-shell effective field theory (OSEFT). This is our starting point to derive small mass corrections to the chiral kinetic theory. In the massless case, only four Wigner functions are needed to describe positive and negative energy fermions of left and right chirality, corresponding to the vectorial components of a fermionic two-point Green's function. As soon as mass correction are introduced, tensorial components are also needed, while the scalar components strictly vanish in the OSEFT. The tensorial components are conveni…
We apply the Wigner-function approach and chiral kinetic theory to investigate the angular momentum and polarization of chiral fluids composed of Weyl fermions with background electric/magnetic fields and vorticity. It is found that the quantum corrections in Wigner functions give rise to nonzero anti-symmetric components in the canonical energy-momentum tensors, which are responsible for the spin-orbit interaction. In global equilibrium, conservation of the canonical angular momentum reveals the cancellation between the orbital component stemming from side jumps with nonzero vorticity and the…
We show that the on-shell effective theory (OSEFT) is the quantum field theory counterpart of a Foldy-Wouthuysen diagonalization of relativistic quantum mechanics for massless fermions. Thus, it is free of the Zitterbewegung oscillations that would yield an ill-defined meaning to the semiclassical transport approach at short distances if derived from the pure Dirac picture. We present a detailed derivation of the collision terms in the chiral kinetic theory using the OSEFT. Collision integrals are derived up to order 1/E, where E is the energy of an on-shell fermion. At this order, the collisi…
We discuss kinetic equations involving the anomalous terms responsible for the chiral anomaly. The general chiral heat wave in cold Fermi liquid is described and the modification of the anomalous zero sound at small temperature and vorticity is found.
We show that Lorentz invariance is realized nontrivially in the classical action of a massless spin-$\frac12$ particle with definite helicity. We find that the ordinary Lorentz transformation is modified by a shift orthogonal to the boost vector and the particle momentum. The shift ensures angular momentum conservation in particle collisions and implies a nonlocality of the collision term in the Lorentz-invariant kinetic theory due to side jumps. We show that 2/3 of the chiral-vortical effect for a uniformly rotating particle distribution can be attributed to the magnetic moment coupling requi…
The second-order nonlinear responses of inviscid chiral fluids near local equilibrium are investigated by applying the chiral kinetic theory (CKT) incorporating side-jump effects. It is shown that the local equilibrium distribution function can be non-trivially introduced in a co-moving frame with respect to the fluid velocity when the quantum corrections in collisions are involved. For the study of anomalous transport, contributions from both quantum corrections in anomalous hydrodynamic equations of motion and those from the CKT and Wigner functions are considered under the relaxation-time (…
We discuss a novel world-line framework for computations of the Chiral Magnetic Effect (CME) in ultrarelativistic heavy-ion collisions. Starting from the fermion determinant in the QCD effective action, we show explicitly how its real part can be expressed as a supersymmetric world-line action of spinning, colored, Grassmanian particles in background fields. Restricting ourselves for simplicity to spinning particles, we demonstrate how their constrained Hamiltonian dynamics arises for both massless and massive particles. In a semi-classical limit, this gives rise to the covariant generalizatio…
In the framework of chiral kinetic theory (CKT), we consider a system of right- and left-handed Weyl fermions out of thermal equilibrium in a homogeneous weak magnetic field. We show that the Lorentz invariance implies a modification in the definition of the momentum current in the phase space, compared to the case in which the system is in global equilibrium. Using this modified momentum current, we derive the linearized conservation equations from the kinetic equation up to second order in the derivative expansion. It turns out that the eigenmodes of these equations, namely the hydrodynamic …
We perform a detailed analysis of the asymptotic behavior of a multifield cosmological model with phantom terms. Specifically, we consider the Chiral-Phantom model consisting of two scalar fields with a mixed kinetic term, while one scalar field has negative kinetic energy, that is, it has phantom properties. We show that the Hubble function can change sign, and we study the global evolution of the field equation in the finite and infinity regions with the use of Poincaré variables. We find that in the Chiral-Phantom model the limit of the quintessence scalar field is recovered while the cosmo…
We argue that in order to study the magneto-transport in a relativistic Weyl fluid, it is needed to take into account the associated quantum corrections, namely the side-jump effect, at least to second order. To this end, we impose Lorentz invariance to a system of free Weyl fermions in the presence of the magnetic field and find the second order correction to the energy dispersion. By developing a scheme to compute the integrals in the phase space, we show that the mentioned correction has non-trivial effects on the thermodynamics of the system. Specifically, we predict the form of the negati…
We construct N=1 supergravity extensions of scalar field theories with higher-derivative kinetic terms. Special attention is paid to the auxiliary fields, whose elimination leads not only to corrections to the kinetic terms, but to new expressions for the potential energy as well. For example, a potential energy can be generated even in the absence of a superpotential. Our formalism allows one to write a supergravity extension of any higher-derivative scalar field theory and, therefore, has applications to both particle physics and cosmological model building. As an illustration, we couple the…
We study the longitudinal magnetotransport in three-dimensional multi-Weyl semimetals, constituted by a pair of (anti)-monopole of arbitrary integer charge ($n$), with $n=1,2$ and $3$ in a crystalline environment. For any $n>1$, even though the distribution of the underlying Berry curvature is anisotropic, the corresponding intrinsic component of the longitudinal magnetoconductivity (LMC), bearing the signature of the chiral anomaly, is insensitive to the direction of the external magnetic field ($B$) and increases as $B^2$, at least when it is sufficiently weak (the semi-classical regime). In…
A kinetic theory can be modified to incorporate triangle anomalies and the chiral magnetic effect by taking into account the Berry curvature flux through the Fermi surface. We show how such a kinetic theory can be derived from underlying quantum field theories. Using the new kinetic theory, we also compute the parity-odd correlation function that is found to be identical to the result in the perturbation theory in the next-to-leading order hard dense loop approximation.
We calculate the most general terms for arbitrary Lagrangians of twisted chiral superfields in 2D (2,2) supersymmetric theories [1]. The scalar and fermion kinetic terms and interactions are given explicitly. We define a set of twisted superspace coordinates, which allows to obtain Lagrangian terms for generic Kähler potential and generic twisted superpotential; this is done in analogy to the corresponding chiral superfields calculations [2]. As examples we obtain the Lagrangian of a single twisted superfield, i.e. the Abelian-dual of the gauged linear sigma model (GLSM) of a single chiral sup…
Extra dimensions (ED) have been used as attempts to explain several phenomena in particle physics over the years. In this paper we investigate the role of an abelian gauge field as mediator of the interaction between dark matter (DM) and Standard Model (SM) particles, in a model with two flat and transverse ED compactified on the chiral square. DM is confined in a thin brane, localized at the origin of the chiral square, while the SM is localized in a finite width brane, lying in the opposite corner of the square. A brane-localized kinetic term is present in the DM brane, while in the fat bran…
We prove that ideal chiral hydrodynamics, as derived from chiral kinetic theory, is acausal and its initial-value problem is ill-posed both in the linearized case around a local equilibrium solution and also in the full nonlinear regime. Therefore, such theory cannot be used to determine how the chiral anomaly affects the hydrodynamic evolution. We show that these fundamental issues can be fixed by using different definitions (frames) for the hydrodynamic fields. This leads to a causal theory of ideal chiral hydrodynamics where the vorticity strength is constrained by the coefficient that enco…
Circularly polarized photons have the Berry curvature in the semiclassical regime. Based on the kinetic equation for such chiral photons, we derive the (non)equilibrium expression of the photon current in the direction of the vorticity. We briefly discuss the relevance of this "photonic chiral vortical effect" in pulsars and rotating massive stars and its possible realization in semiconductors.
We consider cosmological solutions in 5d locally supersymmetric theories including boundary actions, with either opposite tension branes for identical brane chiralities or equal tension branes for flipped brane chiralities. We analyse the occurrence of supersymmetry breakdown in both situations. We find that supersymmetry as seen by a brane observer is broken due to the motion of the brane in the bulk. When the brane energy-momentum tensor is dominated by the brane tension, the 4d vacuum energy cosmological constant on the observable brane is positive and proportional to the inverse square of …
