Index theorem and overlap formalism with naive and minimally doubled fermions

Michael Creutz, Taro Kimura, Tatsuhiro Misumi

Research output: Contribution to journalArticlepeer-review

26 Citations (Scopus)


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.

Original languageEnglish
Article number41
JournalJournal of High Energy Physics
Issue number12
Publication statusPublished - 2010
Externally publishedYes


  • Lattice QCD
  • Lattice gauge field theories
  • Lattice quantum field theory

ASJC Scopus subject areas

  • Nuclear and High Energy Physics


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