Constraints on the Existence of Chiral Fermions in Interacting Lattice Theories

Details Constraints on the Existence of Chiral Fermions in Interacting Lattice Theories Constraints on the Existence of Chiral Fermions in Interacting Lattice Theories

1993-06-29

arxiv.org/abs/hep-lat/9306023v1

Phys.Rev.Lett.71:2691-2694,1993

Physics

High Energy Physics

High Energy Physics - Lattice

LaTeX, 9 pages, WIS--93/56--JUNE--PH

Scientific paper

10.1103/PhysRevLett.71.2691

It is shown that an interacting theory, defined on a regular lattice, must have a vector-like spectrum if the following conditions are satisfied: (a)~locality, (b)~relativistic continuum limit without massless bosons, and (c)~pole-free effective vertex functions for conserved currents. The proof exploits the zero frequency inverse retarded propagator of an appropriate set of interpolating fields as an effective quadratic hamiltonian, to which the Nielsen-Ninomiya theorem is applied.

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