Index Theorem and Overlap Formalism with Naive and Minimally Doubled Fermions

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.

27 pages, 17 figures; references added, version accepted in JHEP

References in corpus (8)

• Four-dimensional graphene and chiral fermions
• Creutz Fermions on an Orthogonal Lattice
• Broken Symmetries from Minimally Doubled Fermions
• Single flavor staggered fermions
• Aoki Phases in the Lattice Gross-Neveu Model with Flavored Mass terms
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Cited by in corpus (5)

• Aoki Phases in the Lattice Gross-Neveu Model with Flavored Mass terms
• Phase structure for lattice fermions with flavored chemical potential terms
• QCD phase diagram with 2-flavor lattice fermion formulations
• Strong-coupling Analysis of Parity Phase Structure in Staggered-Wilson Fermions
• New fermion discretizations and their applications