Gauge-invariant lattice definition of nonabelian chiral gauge theories
In plain words
A grid version exists for chiral theories with the simplest, electromagnetism-like forces. For the non-commuting forces of the Standard Model it is still missing.
Precise statement
For a 4D anomaly-free chiral gauge theory with nonabelian gauge group (for example SU(5) with 5bar + 10, or one Standard Model generation), construct a lattice regularization with exact gauge invariance at finite lattice spacing, a local action and fermion measure, and the correct continuum limit, extending Luscher's 1999 abelian construction based on Ginsparg-Wilson fermions beyond perturbation theory.
What would settle it
An explicit construction with a nonperturbative proof of the locality and gauge invariance of the fermion measure for a nonabelian anomaly-free theory.
Status in the literature
Unverified note: it names recent work and was partly written without a live literature search; it awaits a check by an editor.
The abelian case was completed in 1999 and the nonabelian case to all orders of perturbation theory in 2000; new proposals in 2024-2026 use domain walls with gauge-field flow and symmetry disentanglers.
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