Journal of High Energy Physics

, 2010:27 | Cite as

Renormalization of minimally doubled fermions

  • Stefano Capitani
  • Michael Creutz
  • Johannes Weber
  • Hartmut Wittig


We investigate the renormalization properties of minimally doubled fermions, at one loop in perturbation theory. Our study is based on the two particular realizations of Boriçi-Creutz and Karsten-Wilczek. A common feature of both formulations is the breaking of hyper-cubic symmetry, which requires that the lattice actions are supplemented by suitable counterterms. We show that three counterterms are required in each case and determine their coefficients to one loop in perturbation theory. For both actions we compute the vacuum polarization of the gluon. It is shown that no power divergences appear and that all contributions which arise from the breaking of Lorentz symmetry are cancelled by the counterterms. We also derive the conserved vector and axial-vector currents for Karsten-Wilczek fermions. Like in the case of the previously studied Boriçi-Creutz action, one obtains simple expressions, involving only nearest-neighbour sites. We suggest methods how to fix the coefficients of the counterterms non-perturbatively and discuss the implications of our findings for practical simulations.


Lattice QCD Lattice Gauge Field Theories Global Symmetries 


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Copyright information

© SISSA, Trieste, Italy 2010

Authors and Affiliations

  • Stefano Capitani
    • 1
  • Michael Creutz
    • 1
    • 2
  • Johannes Weber
    • 1
    • 3
  • Hartmut Wittig
    • 1
  1. 1.Institut für Kernphysik, Becher Weg 45University of MainzMainzGermany
  2. 2.Physics DepartmentBrookhaven National LaboratoryUptonU.S.A.
  3. 3.Graduate School of Pure and Applied PhysicsTsukuba UniversityTsukubaJapan

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