A gauge-invariant measure for lattice chiral fermions

Abstract

We nonperturbatively construct a gauge-invariant measure for overlap fermions on four-dimensional Euclidean lattices in a class of nonabelian chiral gauge theories that includes the Standard Model. On admissible gauge fields, comparing chiral projectors at successive lattice spacings yields an exponentially local current and establishes the global properties needed for Lüscher's reconstruction of a smooth, gauge-invariant fermion measure. This provides a candidate nonperturbative lattice definition of the Standard Model.

arXiv comment60+63 pages, 12 figures; three supplementary documents included as ancillary files. Mathematical companion and Lean formalization: https://doi.org/10.5281/zenodo.23196062 . Two-dimensional supplement and calculation records: https://doi.org/10.5281/zenodo.23196101