Index Theorem and Overlap Formalism with Naive and Minimally Doubled Fermions

Understand

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 and the number of species doublers.
• 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.