論文

We study vorticity-induced effects arising from the Wess-Zumino-Witten terms for Nambu-Goldstone modes in chiral perturbation theory. We first provide an alternative derivation of the Wess-Zumino-Witten terms in the presence of external vector, axial-vector, and pseudoscalar fields using a derivative expansion of the fermion determinant. We then employ the previously found correspondence in which vorticity is treated as an axial-vector field coupled to Dirac fermions in flat spacetime. Using this, we derive vorticity-induced contributions for Nambu-Goldstone modes in the presence of electromagnetic fields at finite baryon and isospin chemical potentials, including a vorticity-induced current, a magnetic-field-induced angular momentum, and a vorticity-modified photon–pion coupling. We also briefly discuss the phenomenological implications of these vorticity-induced effects.

We investigate the role of generalized symmetries in driving nonequilibrium and nonlinear phenomena, specifically focusing on turbulent systems. While conventional turbulence studies have revealed inverse cascades driven by conserved quantities integrated over the entire space, such as helicity in three spatial dimensions, the influence of higher-form symmetries, whose conserved charges are defined by integration over subspaces, remains largely unexplored. We demonstrate a novel mechanism where higher-form symmetries naturally induce a self-similar inverse cascade. Taking axion electrodynamics with nonlinear topological interaction as a paradigmatic example, we show that the conserved charge associated with its 1-form symmetry drives the system toward large-scale coherent structures through a universal scaling behavior characterized by analytically determined scaling exponents. Our findings suggest that higher-form symmetries can provide a fundamental organizing principle for understanding nonequilibrium phenomena and the emergence of coherent structures in turbulent systems.

We study the scaling behaviors of the active model B+ using the functional renormalization group (FRG) approach based on the nonequilibrium effective action formulated via the Martin-Siggia-Rose path-integral formalism. We derive the β functions for all couplings of the system in generic d dimensions, revealing regulator independence in various contributions to the renormalization group (RG) flow at specific values for d. After identifying specific regions of the parameter space that define submodels closed under RG transformations, we determine all fixed points of potential physical relevance. We confirm the existence of a bicritical fixed point, which was conjectured within the perturbative momentum-shell RG method for being responsible for the transition from bulk phase separation to microphase separation in active systems. We argue that, within the FRG approach, global flows significantly differ from those obtained in its perturbative counterpart.

We analyze the phase diagram of quantum chromodynamics at low-to-moderate temperature, baryon chemical potential and external magnetic field within chiral perturbation theory at next-to-leading order of the derivative expansion. Our main result is that the anomaly-induced chiral soliton lattice (CSL) phase is stabilized by thermal fluctuations. As a consequence, the CSL state may survive up to temperatures at which chiral symmetry is restored.

We demonstrate the general existence of a local dipole conservation law in bosonic field theory. The scalar charge density arises from the symplectic form of the system, whereas the tensor current descends from its stress tensor. The algebra of spatial translations becomes centrally extended in presence of field configurations with a finite nonzero charge. Furthermore, when the symplectic form is closed but not exact, the system may, surprisingly, lack a well-defined momentum density. This leads to a theorem for the presence of additional light modes in the system whenever the short-distance physics is governed by a translationally invariant local field theory. We also illustrate this mechanism for axion electrodynamics as an example of a system with Nambu–Goldstone modes of higher-form symmetries.

There exist metastable domain walls of the flavor-singlet meson η for the U(1) axial symmetry in two-flavor color superconductivity (2SC) in quantum chromodynamics (QCD) at large baryon density. We show that, due to the coupling of η to confined SU(2) gluons in the 2SC phase, the effective theory on the domain wall is described by the SU(2)-1 Chern-Simons theory, which is dual to the U(1)2 Chern-Simons theory. This theory has a spin-1 droplet excitation that does not carry a baryon number, which we identify as a vector meson. We also discuss the effective theories and baryonic droplet excitations on the domain walls of the flavor-singlet mesons in the superfluid phases of QCD at large isospin density and two-color QCD at large baryon density.

We systematically derive the chiral kinetic theory for chiral fermions with collisions, including the self-energy corrections, from quantum field theories. We find that the Wigner functions and chiral kinetic equations receive both the classical and quantum corrections from the self-energies and their spacetime gradients. We also apply this formalism to study nonequilibrium neutrino transport due to the interaction with thermalized electrons and nucleons, as realized in core-collapse supernovae. We derive neutrino currents along magnetic fields and neutrino spin Hall effect induced by the density gradient at first order in the Fermi constant GF for anisotropic neutrino distributions.

We study the novel asteroseismology of the chiral magnetic wave (CMW) of the quark number density in relativistic quark matter inside neutron stars and core-collapse supernovae and the chiral vortical wave (CVW) of the neutrino number density in relativistic neutrino matter at the core of supernovae. We call the oscillation modes for these chiral waves the chiral magnetic mode (CM-mode) and chiral vortical mode (CV-mode), respectively. We derive the dispersion relations of these new modes in the presence of the chirality flipping due to the finite quark mass and diffusion. We then estimate the possible frequencies of these modes and amplitudes of the resulting gravitational waves. In particular, since the CM-mode can exist only in quark matter with nearly gapless quarks (such as the two-flavor color superconductivity) for a sufficiently strong magnetic field, corresponding gravitational waves provide a new possible probe for such quark matter and the magnetic field in neutron stars.

We develop an approach to chiral kinetic theories for electrons close to equilibrium and neutrinos away from equilibrium based on a systematic power counting scheme for different timescales of electromagnetic and weak interactions. Under this framework, we derive electric and energy currents along magnetic fields induced by neutrino radiation in general nonequilibrium states. This may be regarded as an effective chiral magnetic effect (CME), which is present without a chiral chemical potential, unlike the conventional CME. We also consider the so-called gain region of core-collapse supernovae as an example and find that the effective CME enhanced by persistent neutrino emission in time is sufficiently large to lead to the inverse cascade of magnetic and fluid kinetic energies and observed magnitudes of pulsar kicks. Our framework may also be applicable to other dense-matter systems involving nonequilibrium neutrinos.

We demonstrate a universal mechanism of a class of instabilities in infrared regions for massless Abelian p-form gauge theories with topological interactions, which we call generalized chiral instabilities. Such instabilities occur in the presence of initial electric fields for the p-form gauge fields. We show that the dynamically generated magnetic fields tend to decrease the initial electric fields and result in configurations with linking numbers, which can be characterized by non-invertible global symmetries. The so-called chiral plasma instability and instabilities of the axion electrodynamics and (4+1)-dimensional Maxwell-Chern-Simons theory in electric fields can be described by the generalized chiral instabilities in a unified manner. We also illustrate this mechanism in the (2+1)-dimensional Goldstone-Maxwell model in electric field.

The microscopic quantum nature of elementary particles, chirality, leads to macroscopic phenomena like the chiral anomaly, chiral magnetic effect, and chiral plasma instability. We review recent progress of the studies of these chiral effects in high-energy astrophysics, such as pulsar kicks, magnetars, and core-collapse supernovae, and early Universe cosmology, such as the primordial magnetic field, baryogenesis, and chiral gravitational waves. We also provide a pedagogical introduction to the chiral effects and low-energy effective theories to describe them in and out of equilibrium—the chiral (magneto)hydrodynamics, chiral kinetic theory, and chiral radiation transport theory for neutrinos.

Nambu-Goldstone (NG) modes for 0-form and higher-form symmetries can become unstable in the presence of background fields. Examples include the instability of a photon with a time-dependent axion background or with a chirality imbalance, known as the chiral plasma instability, and the instability of a dynamical axion with a background electric field. We show that all these phenomena can be universally described by a symmetry algebra for 0-form and higher-form symmetries. We prove a counting rule for the number of unstable NG modes in terms of correlation functions of broken symmetry generators. Based on our unified description, we further give a simple new example where one of the NG modes associated with the spontaneous 0-form symmetry breaking U(1)×U(1)→{1} becomes unstable.

Based on quantum field theory, we formulate the Wigner function and quantum kinetic theory for polarized photons in curved spacetimes which admit a covariantly constant timelike vector. From this framework, the photonic chiral/zilch vortical effects are reproduced in a rigidly rotating coordinate. In a spatially inhomogeneous coordinate, we derive the spin Hall effect for the photon helicity current and energy current in equilibrium. Our derivation reveals that such photonic Hall effect are related to the photonic vortical effect via the Lorentz invariance and their transport coefficients match each other.

We investigate polarized gravitational waves generated by chiral fermions in the early Universe. In particular, we focus on the contribution from left-handed neutrinos in thermal equilibrium with finite temperature and chemical potential in the radiation dominated era. We compute the correlation functions of gravitational fields pertinent to the Stokes parameter V characterizing the circular polarization of gravitational waves in the Minkowski and expanding spacetime backgrounds. In the expanding universe, we find that the thermalized neutrinos induce a non-vanishing V linear to the neutrino degeneracy parameter and wavenumber of gravitational waves in the long wavelength region. While the magnitude of the gravitational waves generated by thermal neutrinos is too small to be detectable by current and planned third generation gravitational wave detectors, their observations by future generation detectors for ultra-high frequency regimes could provide information on the neutrino degeneracy parameter in the early Universe.

We show that the backreaction of left-handed neutrinos out of equilibrium on the matter sector induces an electric current proportional to a magnetic field even without a chiral imbalance for electrons in core-collapse supernovae. We derive the transport coefficient of this effect based on the recently formulated chiral radiation transport theory for neutrinos. This chiral electric current generates a strong magnetic field via the so-called chiral plasma instability, which could provide a new mechanism for the strong and stable magnetic field of magnetars. We also numerically study the physical origin of the inverse cascade of the magnetic energy in the magnetohydrodynamics including this current. Our results indicate that incorporating the chiral effects of neutrinos would drastically modify the hydrodynamic evolutions of supernovae, which may also be relevant to the explosion dynamics.

Mass generation of gauge fields can be universally described by topological couplings in gapped systems, such as the Abelian Higgs model in (3+1) dimensions and the Maxwell-Chern-Simons theory in (2+1) dimensions. These systems also exhibit the spontaneous breaking of higher-form Zk symmetries and topological orders for level k≥2. In this paper, we consider topological mass generation in gapless systems. As a paradigmatic example, we study the axion electrodynamics with level k in (3+1) dimensions in background fields that hosts both gapped and gapless modes. We argue that the gapped mode is related to those in fully gapped systems in lower dimensions via dimensional reduction. We show that this system exhibits the spontaneous breaking of a higher-form Zk symmetry despite the absence of the conventional topological order. In the case of the background magnetic field, we also derive the low-energy effective theory of the gapless mode with the quadratic dispersion relation and show that it satisfies the chiral anomaly matching.

Based on the recently formulated chiral radiation transport theory for left-handed neutrinos, we study the chiral transport of neutrinos near thermal equilibrium in core-collapse supernovae. We first compute the near-equilibrium solution of the chiral radiation transport equation under the relaxation time approximation, where the relaxation time is directly derived from the effective field theory of the weak interaction. By using such a solution, we systematically derive analytic expressions for the nonequilibrium corrections of the neutrino energy-momentum tensor and neutrino number current induced by magnetic fields via the neutrino absorption on nucleons. In particular, we find the nonequilibrium neutrino energy current proportional to the magnetic field. We also discuss its phenomenological consequences such as the possible relation to pulsar kicks.

We analyze the combined effects of hydrodynamic fluctuations and chiral magnetic effect (CME) for a chiral medium in the presence of a background magnetic field. Based on the recently developed non-equilibrium effective field theory, we show fluctuations give rise to a CME-related positive contribution to magnetoresistance, while the early studies without accounting for the fluctuations find a CME-related negative magnetoresistance. At zero axial relaxation rate, the fluctuations contribute to the transverse conductivity in addition to the longitudinal one.

What happens to the QCD vacuum when a time-periodic circularly polarized laser field with a sufficiently large intensity and frequency is applied? Based on the Floquet formalism for periodically driven systems and the systematic low-energy effective theory of QCD, we show that for a sufficiently large frequency and above a critical intensity, the QCD vacuum is unstable against the chiral soliton lattice of pions; a crystalline structure of topological solitons that spontaneously breaks parity and continuous translational symmetries. Our work would pave the way for novel “Floquet vacuum engineering.”