The Euler current and relativistic parity odd transport

Abstract

For a spacetime of odd dimensions endowed with a unit vector field, we introduce a new topological current that is identically conserved and whose charge is equal to the Euler character of the even dimensional spacelike foliations. The existence of this current allows us to introduce new Chern-Simons-type terms in the effective field theories describing relativistic quantum Hall states and (2+1) dimensional superfluids. Using effective field theory, we calculate various correlation functions and identify transport coefficients. In the quantum Hall case, this current provides the natural relativistic generalization of the Wen-Zee term, required to characterize the shift and Hall viscosity in quantum Hall systems. For the superfluid case this term is required to have nonzero Hall viscosity and to describe superfluids with non s-wave pairing.

24 pages. v2: added citations, corrected minor typos in appendix

References in corpus (20)

• Two-Dimensional Gas of Massless Dirac Fermions in Graphene
• Experimental Observation of Quantum Hall Effect and Berry's Phase in Graphene
• Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries, and the fractional quantum Hall effect
• Observation of the Fractional Quantum Hall Effect in Graphene
• Fractional quantum Hall effect and insulating phase of Dirac electrons in graphene
• Non-Fermi liquid behaviour of electrons in the half-filled honeycomb lattice (A renormalization group approach)
• Non-Abelian adiabatic statistics and Hall viscosity in quantum Hall states and p_x+ip_y paired superfluids
• Viscosity of Quantum Hall Fluids
• General coordinate invariance and conformal invariance in nonrelativistic physics: Unitary Fermi gas
• Hall Viscosity and Electromagnetic Response
• Hall viscosity, orbital spin, and geometry: paired superfluids and quantum Hall systems
• Quantum critical point in graphene approached in the limit of infinitely strong Coulomb interaction
• Theta-terms in nonlinear sigma-models
• Density-curvature response and gravitational anomaly
• Newton-Cartan Geometry and the Quantum Hall Effect
• Low-Energy Quantum Effective Action for Relativistic Superfluids
• Effective theory of chiral two-dimensional superfluids
• Landau Level Quantization on the Sphere
• Wess-Zumino Terms for Relativistic Fluids, Superfluids, Solids, and Supersolids
• Effective Field Theory of Relativistic Quantum Hall Systems

Cited by in corpus (17)

• Adiabatic hydrodynamics: The eightfold way to dissipation
• Hydrodynamic theory of quantum fluctuating superconductivity
• Effective Field Theory of Relativistic Quantum Hall Systems
• Exact Electromagnetic Response of Landau Level Electrons
• Large Charge Sector of 3d Parity-Violating CFTs
• Chiral $p\pm ip$ superfluid on a sphere
• Geometric Induction in Chiral Superfluids
• Hall viscosity, spin density, and torsion
• Curved-space Dirac description of elastically deformed monolayer graphene is generally incorrect
• Hall viscosity and conductivity of two-dimensional chiral superconductors
• Hall Viscosity in a Strongly Coupled Magnetized Plasma
• Quantum Hall effective action for anisotropic Dirac semi-metal
• Universal nonlinear responses of quantum Hall systems with Galilean invariance
• Euler and Pontryagin currents of the Dirac operator
• Relativistic Gravity and Parity-Violating Non-Relativistic Effective Field Theories
• Effective string theory for vortex lines in fluids and superfluids
• Viscosities and shift in a chiral superfluid: a holographic study