The Euler current and relativistic parity odd transport

  • Siavash Golkar
  • Matthew M. Roberts
  • Dam T. Son
Open Access
Regular Article - Theoretical Physics


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.


Effective field theories Topological States of Matter Space-Time Symmetries 


Open Access

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Copyright information

© The Author(s) 2015

Authors and Affiliations

  • Siavash Golkar
    • 1
  • Matthew M. Roberts
    • 1
  • Dam T. Son
    • 1
  1. 1.Kadanoff Center for Theoretical Physics and Enrico Fermi InstituteUniversity of ChicagoChicagoUnited States

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