A Note On Lattice Definition of Gauge Theories With Chiral Fermions
Abstract
Because of the fermion doubling problem, it has been a longstanding challenge to describe a lattice algorithm for studying four-dimensional gauge theories coupled to chiral fermions. Recently, an algorithm to do so has been described by Craig, extending partial results in the previous literature. Here we describe a variant of this algorithm, based on interpolating a lattice gauge field over the continuum (as in Craig's work) and coupling the interpolated gauge field to continuum chiral fermions. The same variant was also proposed recently by Hsu. In any dimension and for any anomaly-free representation, this approach can be implemented on a computer in principle, but not in practice by Monte Carlo methods because the chiral fermion path integral is not positive.
Related
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BibTeX
@misc{witten2026note,
title = {{A Note On Lattice Definition of Gauge Theories With Chiral Fermions}},
author = {Edward Witten},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.05051},
eprint = {2611.05051},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.05051},
}
RIS
TY - UNPB
TI - A Note On Lattice Definition of Gauge Theories With Chiral Fermions
AU - Edward Witten
PY - 2026
DA - 2026/11/03
PB - arXiv
DO - 10.48550/arxiv.2611.05051
UR - https://arxiv.org/abs/2611.05051
AB - Because of the fermion doubling problem, it has been a longstanding challenge to describe a lattice algorithm for studying four-dimensional gauge theories coupled to chiral fermions. Recently, an algorithm to do so has been described by Craig, extending partial results in the previous literature. Here we describe a variant of this algorithm, based on interpolating a lattice gauge field over the continuum (as in Craig's work) and coupling the interpolated gauge field to continuum chiral fermions. The same variant was also proposed recently by Hsu. In any dimension and for any anomaly-free representation, this approach can be implemented on a computer in principle, but not in practice by Monte Carlo methods because the chiral fermion path integral is not positive.
ER -