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)

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• Single flavor staggered fermions
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• Equivalence of lattice operators and graph matrices
• New conjecture on exact Dirac zero-modes of lattice fermions
• New fermion discretizations and their applications
• Symanzik effective action for Karsten-Wilczek minimally doubled fermions
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• Lattice fermion formulation via Physics-Informed Neural Networks: Ginsparg-Wilson relation and Overlap fermions
• Index theorem with Minimally Doubled Fermions in four space-time dimensions
• Twisted 3D $N=4$ Supersymmetric YM on deformed ${\mathbb{A}}_3^{\ast }$ Lattice
• Topological properties of minimally doubled fermions in two space-time dimensions