Index Theorem and Overlap Formalism with Naive and Minimally Doubled Fermions

Details Index Theorem and Overlap Formalism with Naive and Minimally Doubled Fermions Index Theorem and Overlap Formalism with Naive and Minimally Doubled Fermions

2010-11-02

arxiv.org/abs/1011.0761v2

JHEP 1012:041,2010

Physics

High Energy Physics

High Energy Physics - Lattice

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

Scientific paper

10.1007/JHEP12(2010)041

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.

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