nucl-th digest · Sep 5, 2019

[Submitted on 4 Sept 2019] (cross-list from hep-th)

Chiral Waves on the Fermi-Dirac Sea: Quantum Superfluidity and the Axial Anomaly

We show that as a result of the axial anomaly, massless fermions at zero temperature define a relativistic quantum superfluid. The anomaly pole implies the existence of a gapless Chiral Density Wave (CDW), i.e. an axion-like acoustic mode of an irrotational and dissipationless Hamiltonian perfect fluid, that is a correlated fermion/anti-fermion pair excitation of the Fermi-Dirac sea. In $D = 2$ dimensions the chiral superfluid effective action coincides with that of the Schwinger model as $e \to 0$ , and the CDW acoustic mode is precisely the Schwinger boson. Since this identity holds also at zero chiral chemical potential, the Dirac vacuum itself may be viewed as a quantum superfluid state. The CDW collective boson is a $U (1)$ chiral phase field, which is gapless as a result of a novel, non-linear realization of Goldstone's theorem, extended to this case of symmetry breaking by an anomaly. A new local form of the axial anomaly bosonic effective action in any $D$ even spacetime is given, consistent with superfluidity, and its quantization is shown to be required by the anomalous Schwinger terms in fermion current commutators. In QED $_{4}$ this collective Goldstone mode appears as a massless pole in the axial anomaly triangle diagram, and is responsible for the macroscopic non-dissipative currents of the Chiral Magnetic and Chiral Separation Effects, as well as the Anomalous Hall Effect. In a constant uniform magnetic field an exact dimensional reduction from $D = 4$ to $D = 2$ occurs and the collective $e^{+} e^{-}$ CDW chiral pair excitation propagating along the magnetic field direction is a Chiral Magnetic Wave, which acquires a mass gap $M^{2} = e^{3} B /2 π^{2}$ . Possible realizations and tests of the theory of collective bosonic excitations due to the anomaly in Dirac/Weyl materials are briefly discussed.

Comments:: Journal version, 54 pages, 2 figures, references added
Subjects:: High Energy Physics — Theory (hep-th); Nuclear Theory (nucl-th)
arXiv:: 1909.01974 [pdf]

NPB(2021)·15 citations

Thursday·September 5, 2019

A Particle Emitting Source From an Accelerating, Perturbative Solution of Relativistic Hydrodynamics

Chiral Waves on the Fermi-Dirac Sea: Quantum Superfluidity and the Axial Anomaly

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