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Constraints on the Existence of Chiral Fermions in Interacting Lattice Theories
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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.
Forward citations
Cited by 2 Pith papers
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Fermionic Villain model with exact lattice chiral symmetries
A fermionic Villain lattice Hamiltonian exactly realizes the chiral U(1) L x U(1) R symmetry and anomalies of a massless Dirac fermion, enabling exact studies of symmetric mass generation and chiral lattice gauge theories.
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Bosonization versus the Nielsen-Ninomiya theorem
The 2D modified Villain model's Weyl operators reproduce free Dirac correlations in the continuum, and their no-doubler Dirac kernel is non-local, showing exactly how bosonization evades the Nielsen-Ninomiya theorem.
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