Weyl fermions on a finite lattice

Author:

David B. Kaplan, Sriyomee Sen

Keyword:

High Energy Physics - Lattice, High Energy Physics - Lattice (hep-lat), Strongly Correlated Electrons (cond-mat.str-el), High Energy Physics - Theory (hep-th)

journal:

INT-PUB-23-046

date:

2023-12-07 00:00:00

Abstract

The phenomenon of unpaired Weyl fermions appearing on the sole 2n-dimensional boundary of a (2n + 1)-dimensional manifold with massive Dirac fermions was recently analyzed recently. In this Letter we show that similar unpaired Weyl edge states can be seen on a finite lattice. In particular, we consider the discretized Hamiltonian for a Wilson fermion in (2+1) dimensions with a 1+1 dimensional boundary and continuous time. We demonstrate that the low lying boundary spectrum is indeed Weyl-like: it has a linear dispersion relation, definite chirality, and circulates only in one direction around the boundary. We comment on how our results are consistent with Nielsen-Ninomiya theorem. This work removes one potential obstacle facing the program recently outlined by one of the authors for regulating chiral gauge theories.

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