Local CP-violation and electric charge separation by magnetic fields from lattice QCD

  • G. S. Bali
  • F. Bruckmann
  • G. Endrődi
  • Z. Fodor
  • S. D. Katz
  • A. Schäfer
Open Access


We study local CP-violation on the lattice by measuring the local correlation between the topological charge density and the electric dipole moment of quarks, induced by a constant external magnetic field. This correlator is found to increase linearly with the external field, with the coefficient of proportionality depending only weakly on temperature. Results are obtained on lattices with various spacings, and are extrapolated to the continuum limit after the renormalization of the observables is carried out. This renormalization utilizes the gradient flow for the quark and gluon fields. Our findings suggest that the strength of local CP-violation in QCD with physical quark masses is about an order of magnitude smaller than a model prediction based on nearly massless quarks in domains of constant gluon backgrounds with topological charge. We also show numerical evidence that the observed local CP-violation correlates with spatially extended electric dipole structures in the QCD vacuum.


Quark-Gluon Plasma Lattice QCD Lattice Gauge Field Theories Lattice Quantum Field Theory 


Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.


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Copyright information

© The Author(s) 2014

Authors and Affiliations

  • G. S. Bali
    • 1
    • 2
  • F. Bruckmann
    • 1
  • G. Endrődi
    • 1
  • Z. Fodor
    • 3
    • 4
    • 5
  • S. D. Katz
    • 4
    • 6
  • A. Schäfer
    • 1
  1. 1.Institute for Theoretical PhysicsUniversität RegensburgRegensburgGermany
  2. 2.Tata Institute of Fundamental ResearchMumbaiIndia
  3. 3.Bergische Universität Wuppertal, Theoretical PhysicsWuppertalGermany
  4. 4.Eötvös University, Theoretical PhysicsBudapestHungary
  5. 5.Jülich Supercomputing Centre, Forschungszentrum JülichJülichGermany
  6. 6.MTA-ELTE Lendület Lattice Gauge Theory Research GroupBudapestHungary

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