<p>We establish thermodynamic stability and gauge invariance in the magnetovortical matter of Dirac fermions under the coexistent rotation and strong magnetic field. The corresponding partition function reveals that the orbital contribution to bulk thermodynamics preponderates over the conventional contribution from anomaly-related spin effects. This orbital preponderance macroscopically manifests itself in the sign inversion of the induced charge and current in the magnetovortical matter, and can be tested experimentally as the flip of the angular momentum polarization of magnetovortical matter when the magnetic field strength is increased.</p>

Japan

Kenji Fukushima

China

Koichi Hattori

Kazuya Mameda

Preponderant Orbital Polarization in Relativistic Magnetovortical Matter

Abstract Based on the functional renormalization group (FRG) under the local potential approximation, we analyze the Bose–Einstein condensation (BEC) in the relativistic complex scalar theory. This framework leads to a complex flow equation of the effective potential, even with the well-known Litim regulator. In order to evaluate the condensate from such a complex effective potential, we impose a condition between chemical potential and mass, analogously to those in the free theory or the mean field theory. We elucidate that for the strongly (weakly) coupled theory, the phase diagrams computed from the FRG are more (less) deviated from that under the mean field approximation. This result implies that quantum fluctuations strongly affect the nonperturbative formation of the BEC.

Fumio Terazaki

Katsuhiko Suzuki

Relativistic BEC extracted from a complex FRG flow equation

We revisit the condensation scenario of charged pions in external magnetic field and rotation, which was first considered by Y. Liu and I. Zahed. Based on the Ginzburg-Landau analysis of the Nambu-Jona-Lasinio model, we find that the charged-pion condensation takes place only when both a strong coupling constant and negatively large baryon chemical potential are applied. Besides, our numerical calculation shows that the chiral restoration induced by the interplay between magnetic field and rotation (i.e., the rotational magnetic inhibition) interrupts the formation of the charged-pion condensate. This suggests that the analysis of such condensation requires a careful treatment of the inner structure of pions, which was not taken into account before. We also discuss the underlying physical mechanism of our finding and the indication of charged-rho condensation.

Hao-Lei Chen

Xu-Guang Huang

Do charged-pions condense in a magnetic field with rotation?

Based on the bag model, we revisit the deconfinement phase transition under rotation. On top of the usual rotational energy for noninteracting particles, we perturbatively analyze the revolution effect of the hadron bag, i.e., of the potential confining quarks. The revolution effect can be phenomenologically translated into the rotational correction to the QCD vacuum energy or the gluon condensate. We demonstrate that if the revolution effect is (is not) taken into account, the transition temperature increases (decreases) as the angular velocity increased. The ‘revolving bag model’ provides a feasible explanation of the recent lattice simulations showing, contrary to effective models, that rotation favors the confined phase.

Keiya Takizawa

Deconfinement transition in the revolving bag model

From quantum field theory, we derive the chiral kinetic theory involving nonlinear quantum corrections coupled with spacetime-dependent electromagnetic fields and fluid velocity gradients. An equilibrium Wigner function determined by the kinetic equation verifies the nondissipativeness of the charge induced by the magneto-vortical coupling. We reveal that this nonlinear chiral kinetic theory is consistent with the one-loop Euler–Heisenberg effective theory, indicating an indirect evidence of the trace anomaly in the kinetic theory. We also argue a potential issue on the regularization, and demonstrate the availability of the point-splitting regularization in the nonlinear chiral kinetic theory.

Nonlinear chiral kinetic theory

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.

Naoki Yamamoto

Taiwan

Di-Lun Yang

Photonic spin Hall effect from quantum kinetic theory in curved spacetime

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.

Tomoya Hayata

Yoshimasa Hidaka

Second order chiral kinetic theory under gravity and antiparallel charge-energy flow

We develop a covariant kinetic theory for massive fermions in a curved spacetime and an external electromagnetic field based on quantum field theory. We derive four coupled semi-classical kinetic equations accurate to 
					, which describe the transports of particle number and spin degrees of freedom. The relationship with chiral kinetic theory is discussed. As an application, we study spin polarization in the presence of finite Riemann curvature and an electromagnetic field in both local and global equilibrium states.
				

Yu-Chen Liu

Covariant spin kinetic theory I: collisionless limit X.-G. H. was supported by NSFC (11535012, 11675041), and K. M. was supported by the China Postdoctoral Science Foundation (2017M621345)

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 in a background curved geometry. The resultant framework is U(1) gauge invariant and local Lorentz and diffeomorphism covariant. It is particularly useful to study the gravitational or noninertial effects for chiral fermions. As the first application, we study the chiral dynamics in a rotating coordinate and clarify the roles of the Coriolis force and spin-vorticity coupling in generating the chiral vortical effect. We also show that the chiral vortical effect is an intrinsic phenomenon of a rotating chiral fluid, and thus independent of the observer’s frame.

Lan-Lan Gao

Chiral kinetic theory in curved spacetime

We discuss the importance of boundary effects on fermionic matter in a rotating frame. By explicit calculations at zero temperature we show that the scalar condensate of fermion and anti-fermion cannot be modified by the rotation once the boundary condition is properly implemented. The situation is qualitatively changed at finite temperature and/or in the presence of a sufficiently strong magnetic field that supersedes the boundary effects. Therefore, to establish an interpretation of the rotation as an effective chemical potential, it is crucial to consider further environmental effects such as the finite temperature and magnetic field.