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Journal of High Energy Physics

, 2010:41 | Cite as

Index theorem and overlap formalism with naive and minimally doubled fermions

  • Michael Creutz
  • Taro Kimura
  • Tatsuhiro Misumi
Article

Abstract

We present a theoretical foundation for the Index theorem in naive and minimally doubled lattice fermions by studying the spectral flow of a Hermitean version of Dirac operators. We utilize the point splitting method to implement flavored mass terms, which play an important role in constructing proper Hermitean operators. We show the spectral flow correctly detects the index of the would-be zero modes which is determined by gauge field topology. Using the flavored mass terms, we present new types of overlap fermions from the naive fermion kernels, with a number of flavors that depends on the choice of the mass terms. We succeed to obtain a single-flavor naive overlap fermion which maintains hypercubic symmetry.

Keywords

Lattice Gauge Field Theories Lattice Quantum Field Theory Lattice QCD 

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Copyright information

© SISSA, Trieste, Italy 2010

Authors and Affiliations

  1. 1.Physics DepartmentBrookhaven National LaboratoryUptonU.S.A.
  2. 2.Department of Basic ScienceUniversity of TokyoTokyoJapan
  3. 3.Yukawa Institute for Theoretical PhysicsKyoto UniversityKyotoJapan

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