Chiral Vortical Effect Research Articles

A non-perturbative mixed anomaly and fractional hydrodynamic transport

We present a new non-perturbative ’t Hooft anomaly afflicting a quantum field theory with symmetry group G = U(1) × ℤ2 in four dimensions. We use the Adams spectral sequence to compute that the bordism group \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\Omega }_{5}^{{\ ext{Spin}}}$$\\end{document}(BG), which classifies anomalies that remain when perturbative anomalies cancel, is ℤ4. By constructing a mapping torus and evaluating the Atiyah-Patodi-Singer η-invariant, we show that the mod 4 anomaly is generated by a pair of Weyl fermions that are vector-like under U(1), but with only one component charged under ℤ2. We construct a simple microscopic field theory that realises the anomaly, before investigating its impact in the hydrodynamic limit. We find that the anomaly dictates transport phenomena in the U(1) current and energy-momentum tensor akin to the chiral vortical and magnetic effects (even though the perturbative anomalies here vanish), but with the conductivities being fractionally quantised in units of a quarter, reflecting the mod 4 nature of the bordism group. Along the way, we compute the (relevant) bordism groups \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\Omega }_{d}^{{\ ext{Spin}}}$$\\end{document}(Bℤ2 × BU(1)) and \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\Omega }_{d}^{{{\ ext{Pin}}}^{-}}$$\\end{document} (BU(1)) in all degrees d = 0 through 5.

Domain-wall Skyrmion phase in a rapidly rotating QCD matter

Based on the chiral perturbation theory at the leading order, we show a signal of the presence of a new phase in rapidly rotating QCD matter with two flavors, that is a domain-wall Skyrmion phase. Based on the chiral Lagrangian with a Wess-Zumino-Witten (WZW) term responsible for the chiral anomaly and chiral vortical effect, it was shown that the ground state is a chiral soliton lattice (CSL) consisting of a stack of η-solitons in a high density region under rapid rotation. In a large parameter region, a single η-soliton decays into a pair of non-Abelian solitons, each of which carries SU(2)V/U(1) ≃ ℂP1 ≃ S2 moduli as a consequence of the spontaneously broken vector symmetry SU(2)V. In such a non-Abelian CSL, we construct the effective world-volume theory of a single non-Abelian soliton to obtain a d = 2 + 1 dimensional ℂP1 model with a topological term originated from the WZW term. We show that when the chemical potential is larger than a critical value, a topological lump supported by the second homotopy group π2(S2) ≃ ℤ has negative energy and is spontaneously created, implying the domain-wall Skyrmion phase. This lump corresponds in the bulk to a Skyrmion supported by the third homotopy group π3[SU(2)] ≃ ℤ carrying a baryon number. This composite state is called a domain-wall Skyrmion, and is stable even in the absence of the Skyrme term. An analytic formula for the effective nucleon mass in this medium can be written only in terms of the meson’s constants as 42πfπfη/mπ~1.21\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ 4\\sqrt{2}\\pi {f}_{\\pi }{f}_{\\eta }/{m}_{\\pi}\\sim 1.21 $$\\end{document} GeV with the decay constants fπ and fη of the pions and η meson, respectively, and the pion mass mπ. This is reasonably heavier than the nucleon mass in the QCD vacuum.

Non-perturbative suppression of chiral vortical effect in hot (s)QGP for hyperons spin polarization in heavy ion collisions

With the field correlator method (FCM) for QCD, we show that the chiral vortical effect (CVE) in hot (strongly-interacting) quark-gluon plasma ((s)QGP) is modified by non-perturbative interactions – by color-magnetic confinement, and by remnant color-electric interaction, which is encoded in the Polyakov line. The obtained result demonstrates numerical suppression of CVE comparable to the phenomenological suppression used for numerical simulations of RHIC-STAR data on hyperons spin polarization in non-central heavy ion collision (HIC). The parameters range in the temperature – quark chemical potential plane is expected to cover ALICE and RHIC data. The chiral current is calculated for the rigidly rotating model of (s)QGP in the linear order in angular velocity at the rotation axis with account of non-perturbative interactions.

Search for anomalous chiral effects in heavy-ion collisions with ALICE

The interplay between the chiral anomaly and the strong magnetic or vortical fields created in noncentral heavy-ion collisions can lead to various anomalous chiral effects in the quark–gluon plasma, including the chiral magnetic effect (CME), the chiral magnetic wave (CMW), and the chiral vortical effect (CVE). In this proceeding, recent ALICE measurements of these effects are summarized. Utilizing Event Shape Engineering, fractions of CME and CMW signals extracted in Pb–Pb collisions at √SNN = 5.02 TeV are consistent with zero within uncertainties. The CVE is studied using azimuthal correlations between baryon pair Λ–p with Λ–h and h–h as reference. These measurements provide new insights into the experimental search for anomalous chiral effects in heavy-ion collisions.

Search for the chiral magnetic and vortical effects using event shape approaches in Au+Au collisions at STAR

The chiral magnetic/vortical effect (CME/CVE) in heavy-ion collisions probes the topological sector of Quantum Chromodynamics, where P and CP symmetries are violated locally in strong interactions. However, the experimental observables for the CME/CVE are dominated by backgrounds related to elliptic flow and nonflow. We employ event shape approaches to mitigate the flow background and event planes based on spectators to minimize the nonflow background. We report on the CME search in Au+Au collisions at √SNN = 7.7, 14.6, 19.6, 27, and 200 GeV, as well as the CVE search at 19.6 and 27 GeV.

Anomalous transport from geometry

We revisit the relation between black hole geometries and chiral transport. Integrating the anomaly equation in a black hole geometry allows us to derive the chiral transport coefficients for the thermal gas far from the horizon. The key ingredient is to impose vanishing of the covariant current on the horizon. We extend the method to include the usual gauge anomaly for charged black holes and to weak magnetic fields. This allows us to derive the full set of transport coefficients describing the chiral magnetic and chiral vortical effects.

Vortical effects in chiral band structures

The chiral vortical effect is a chiral anomaly-induced transport phenomenon characterized by an axial current in a uniformly rotating chiral fluid. It is well understood for Weyl fermions in high energy physics, but its realization in condensed matter band structures, including those of Weyl semimetals, has been controversial. In this work, we develop the Kubo response theory for electrons in a general band structure subject to space- and time-dependent rotation or vorticity relative to the background lattice. For continuum Hamiltonians, we recover the chiral vortical effect in the static limit and the transport or uniform limit when the fluid, strictly, is not a Fermi liquid. In the transport limit of a Fermi liquid, we describe an effect that we dub the gyrotropic vortical effect. The latter is governed by Berry curvature of the occupied bands while the former contains an additional contribution from the magnetic moment of electrons on the Fermi surface. The two vortical effects can be understood as kinematic analogs of the well-known chiral and gyrotropic magnetic effects in chiral band structures. We address recent controversies in the field and conclude by describing device geometries that exploit Ohmic or Seebeck transport to drive the vortical effects.

Tilt-induced vortical response and mixed anomaly in inhomogeneous Weyl matter

We propose a nondissipative transport effect and vortical response in Weyl semimetals in the presence of spatial inhomogeneities, namely, a spatially varying tilt of the Weyl cones. We show that when the spectrum is anisotropic and tilted due to spatial lattice variations, one is confronted with generalized quantum anomalies due to the effective fields stemming from the tilt structure. In particular, we demonstrate that the position-dependent tilt parameter induces local vorticity, thus generating a chiral vortical effect even in the absence of rotation or magnetic fields. As a consequence, it couples to the electric field and thus contributes to the anomalous Hall effect.

Progress on the experimental search for the chiral magnetic effect, the chiral vortical effect, and the chiral magnetic wave

In quantum chromodynamics, the interactions of quarks with the topological gluon field can lead to nonconservation of local parity (P) and conjugated parity (CP) , which provides a solution to the strong CP problem and a possibility to explain the asymmetry of matter-antimatter in the current universe. Under the action of a strong magnetic field, the nonconservation of P and CP can lead to the separation of particles according to their electric charges, which is called the chiral magnetic effect (CME). An observation of the CME-induced charge separation will confirm several fundamental properties of quantum chromodynamics (QCD), namely, approximate chiral symmetry restoration, topological charge fluctuation, and local parity violation. In relativistic heavy-ion collisions, there are other chiral anomalous effects similar to the CME, such as the chiral vortical effect (CVE) and the chiral magnetic wave (CMW). This review briefly summarizes the current progress of experimental research on the CME, CVE, and CMW in relativistic heavy-ion collisions.

Medium Correction to Gravitational Form Factors

We generalize the gravitational form factor for chiral fermion in vacuum, which reproduces the well-known spinvorticity coupling. We also calculate radiative correction to the gravitational form factors in quantum electrodynamics plasma. We find two structures in the form factors contributing to the scattering amplitude of fermion in vorticity field, one is from the fermon self-energy correction, pointing to suppression of spin-vorticity coupling in medium; the other strucutre comes from graviton-fermion vertex correction, which does not adopt potential interpretation, but corresponds to transition matrix element between initial and final states. Both structures contribute to chiral vortical effect. The net effect is that radiative correction enhances the chiral vortical effect. Our results claify the relation and difference between spin-vorticity coupling and chiral vortical effect from the perspective of form factors. We also discuss the application of the results in QCD plasma, indicating radiative correction might have an appreciable effect in spin polarization effect in heavy ion collisions.

Medium correction to gravitational form factors

We generalize the gravitational form factor for chiral fermion in vacuum, which reproduces the well-known spin-vorticity coupling. We also calculate radiative correction to the gravitational form factors in quantum electrodynamics plasma. We find two structures in the form factors contributing to the scattering amplitude of fermion in vorticity field, one is from the fermon self-energy correction, pointing to suppression of spin-vorticity coupling in medium; the other strucutre comes from graviton-fermion vertex correction, which does not adopt potential interpretation, but corresponds to transition matrix element between initial and final states. Both structures contribute to chiral vortical effect. The net effect is that radiative correction enhances the chiral vortical effect. Our results claify the relation and difference between spin-vorticity coupling and chiral vortical effect from the perspective of form factors. We also discuss the application of the results in QCD plasma, indicating radiative correction might have an appreciable effect in spin polarization effect in heavy ion collisions.

Axial chiral vortical effect in a sphere with finite size effect* *Supported by the National Key Research and Development Program of China (2022YFA1604900) and the National Natural Science Foundation of China (11735007, 11890710, 11890711, 11890713, 12275104)

We investigate the axial vortical effect in a uniformly rotating sphere subject to finite size. We use the MIT boundary condition to limit the boundary of the sphere. For massless fermions inside the sphere, we obtain the exact axial vector current far from the boundary that matches the expression obtained in cylindrical coordinates in literature. On the spherical boundary, we find both the longitudinal and transverse (with respect to the rotation axis) components with magnitude depending on the colatitude angle. For massive fermions, we derive an expansion of the axial conductivity far from the boundary to all orders of mass, whose leading order term agrees with the mass correction reported in literature. We also obtain the leading order mass correction on the boundary, which is linear and stronger than the quadratic dependence far from the boundary. The qualitative implications on the phenomenology of heavy ion collisions are speculated.

Shear-induced anomalous transport and charge asymmetry of triangular flow in heavy-ion collisions

Chiral anomaly implies the existence of non-dissipative transport phenomena, such as the chiral magnetic effect. At second order in the derivative expansion, novel quantum transport phenomena emerge. In this paper, we focus on the anomalous transport driven by a combination of shear, vorticity and magnetic field. We find that the corresponding transport phenomena -- shear-induced chiral magnetic and chiral vortical effects (siCME and siCVE) -- induce characteristic charge correlations among the hadrons produced in heavy ion collisions. We propose the charge asymmetry of triangular flow as a signature of the anomalous transport, and estimate the strength of the signal, as well as the background, using hydrodynamical model simulations. We find that the signal-to-background ratio for the proposed observable is favorable for experimental detection.

Chiral Vortical Effect for Spin 3/2

Chiral Vortical Effect for Spin 3/2

Quantum nucleation of topological solitons

The chiral soliton lattice is an array of topological solitons realized as ground states of QCD at finite density under strong magnetic fields or rapid rotation, and chiral magnets with an easy-plane anisotropy. In such cases, topological solitons have negative energy due to topological terms originating from the chiral magnetic or vortical effect and the Dzyaloshinskii-Moriya interaction, respectively. We study quantum nucleation of topological solitons in the vacuum through quantum tunneling in 2 + 1 and 3 + 1 dimensions, by using a complex ϕ4 (or the axion) model with a topological term proportional to an external field, which is a simplification of low-energy theories of the above systems. In 2 + 1 dimensions, a pair of a vortex and an anti-vortex is connected by a linear soliton, while in 3 + 1 dimensions, a vortex is string-like, a soliton is wall-like, and a disk of a soliton wall is bounded by a string loop. Since the tension of solitons can be effectively negative due to the topological term, such a composite configuration of a finite size is created by quantum tunneling and subsequently grows rapidly. We estimate the nucleation probability analytically in the thin-defect approximation and fully calculate it numerically using the relaxation (gradient flow) method. The nucleation probability is maximized when the direction of the soliton is perpendicular to the external field. We find a good agreement between the thin-defect approximation and direct numerical simulation in 2 + 1 dimensions if we read the vortex tension from the numerics, while we find a difference between them at short distances interpreted as a remnant energy in 3 + 1 dimensions.

Nonrelativistic transport theory from vorticity dependent quantum kinetic equation

We study the three-dimensional transport theory of massive spin-1/2 fermions resulting from the vorticity dependent quantum kinetic equation. This quantum kinetic equation has been introduced to take account of noninertial properties of rotating coordinate frames. We show that it is the appropriate relativistic kinetic equation which provides the vorticity dependent semiclassical transport equations of the three-dimensional Wigner function components. We establish the semiclassical kinetic equations of a linearly independent set of components. By means of them, kinetic equations of the chiral scalar distribution functions are derived. They furnish the 3D kinetic theory which permits us to study the vector and axial vector current densities by focusing on the mass corrections to the chiral vortical and separation effects.

Anomalous chiral transport with vorticity and torsion: Cancellation of two mixed gravitational anomaly currents in rotating chiral p+ip Weyl condensates

Relativistic gravitational anomalies lead to anomalous transport coefficients that can be activated at finite temperature in condensed matter systems with gapless fermions. The chiral vortical effect (CVE) is an anomalous chiral current along a rotation axis, expressed in terms of a gravimagnetic field and a gravitational anomaly. Another one, the chiral torsional effect (CTE), arises from hydrodynamically independent frame fields and connection. We discuss the relation of CVE, CTE and gravitational anomalies for relativistic fermions from the perspective of torsion and the Nieh-Yan anomaly. The DC transport coefficients of the two anomalies are found to be closely related depending whether or not torsion is non-zero in the hydrodynamics. The relativistic anomaly from torsion is well defined if instead of an ultraviolet divergent term, the chemical potential or temperature enter. The anomaly term is 2nd order in gradients and contributes in linear response for CTE, implying also the same for CVE. As an example, we consider chiral $p+ip$ Weyl superfluids/conductors. At low-energies, the system is effectively relativistic along a special anisotropy axis. The hydrodynamics is governed by two velocities, normal velocity $\boldsymbol{v}_n$ and superfluid velocity $\boldsymbol{v}_s$. The two anomalies follow from the normal component rotation and the dependence of the momentum density on the superfluid velocity (order parameter). In the CVE the chiral current is produced by solid body rotation of the normal component with (angular) velocity $\boldsymbol{v}_n= \boldsymbol\Omega \times \boldsymbol{r}$. In the CTE, a chiral current is produced the vorticity $\nabla \times \boldsymbol{v}_s$, which in the low-energy effective theory is torsion. In equilibrium, $\langle\langle \nabla \times \boldsymbol{v_s}\rangle\rangle= 2\boldsymbol\Omega$ on average and the two anomaly currents cancel.

Chiral vortical effect in extended Rarita-Schwinger field theory and chiral anomaly

We consider the theory of Rarita-Schwinger field interacting with a field with spin 1/2, in the case of finite temperature, chemical potential and vorticity, and calculate the chiral vortical effect for spin 3/2. We have clearly demonstrated the role of interaction with the spin 1/2 field, the contribution of the terms with which to CVE is 6. Since the contribution from the Rarita-Schwinger field is -1, the overall coefficient in CVE is 6-1=5, which corresponds to the recent prediction of a gauge chiral anomaly for spin 3/2. The obtained values for the coefficients $\mu^2$ and $T^2$ are proportional to each other, but not proportional to the spin, which indicates a possible new universality between the temperature-related and the chemical potential-related vortical effects. The results obtained allow us to speculate about the relationship between the gauge and gravitational chiral anomalies.

Hyperon\u2013anti-hyperon polarization asymmetry in relativistic heavy-ion collisions as an interplay between chiral and helical vortical effects

We argue that the enhancement in the spin polarization of anti-hyperons compared to the polarization of the hyperons in noncentral relativistic heavy-ion collisions arises as a result of an interplay between the chiral and helical vortical effects. The chiral vortical effect generates the axial current of quarks along the vorticity axis while the recently found helical vortical effect generates the helicity flow – the projection of the quark’s polarization vector onto its momentum – along the same axis. For massless fermions, the helical charge corresponds to a difference in the contributions of particles and anti-particles to the axial charge. Assuming that the spin of light quarks transfers to the strange quarks via the vector kaon states (“the spin-vector dominance”), we are able to describe the ratio of the (anti)hyperon spin polarizations, obtained by the STAR group, without fitting parameters. We also argue that the helical vortical effect dominates over the chiral vortical effect and the chiral magnetic effect in the generation of the electric current.

Chiral vortical effect in accelerated matter

We revisit evaluation of the chiral vortical effect in accelerated matter. To first order in the acceleration the corresponding matrix element of the axial current can be reconstructed from its flat-space limit. A crucial point is existence of an extra conservation law of fluid helicity which is not related to the symmetry of the Lagrangian. As a result, one can reproduce, via the equivalence principle, the effect of the so-called gravimagnetic anomaly; resolving in this way a long standing puzzle of its interpretation. Moreover, as a consequence of the extra conservation law the microscopic axial charge and helicity of the macroscopic motion are separately conserved. Some further consequences from the matching of the equivalence principle with hydrodynamics concerning higher orders in gradient expansion or in the acceleration are briefly discussed.