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Gauge-invariant measures for lattice chiral fermions

For SU(5) overlap fermions in representation 10⊕5̄ on finite periodic four-dimensional Euclidean lattices, can one construct a smooth exponentially local measure current solving the anomaly equation and satisfying full integrability on admissible gauge fields? The target is a gauge-invariant measure on every nonempty component, up to a constant phase, with restrictions to the four specified global forms of the Standard Model gauge group.

Why it matters and what counts as progress

Why it matters: It addresses the obstruction to constructing a local gauge-invariant nonperturbative measure for the stated chiral gauge theories.

What counts as progress: Construct the local anomaly-solving measure current and prove global integrability on every admissible component for the specified representations.

How the problem developed

  1. 25 Nov 1998 · Partial result [1]

    Martin Lüscher Constructed an exact gauge-invariant measure for anomaly-free U(1) chiral gauge theories on the lattice, a restricted setting within the wider nonabelian problem.

  2. 6 Oct 2026 · Reported claim [2]

    Nathaniel Craig and GPT-6 Astra The paper reports a nonperturbative gauge-invariant measure for overlap fermions on finite four-dimensional lattices in a class of nonabelian theories including the Standard Model; the paper credits GPT-6 Astra with the central strategy and proof, with human direction and checking.

AI contribution

A gauge-invariant measure for lattice chiral fermions

Nathaniel Craig

For SU(5) overlap fermions in the representation 10⊕5̄ on finite periodic four-dimensional Euclidean lattices, the paper constructs a smooth exponentially local measure current satisfying the anomaly equation and full integrability on admissible gauge fields. It reconstructs a gauge-invariant measure on every nonempty component, up to a constant phase, and restricts it to the four stated global forms of the Standard Model gauge group.

AI involvementAI-led
ImportanceMajor
Technical verificationFormal (Lean)
Human understandingFew
Paper date:

Read the contribution and its assessment →

Sources

  1. Martin Lüscher, Exact chiral symmetry on the lattice and the Ginsparg-Wilson relation
  2. Craig: lattice chiral-fermion construction and AI disclosure
  3. Craig: exact formalization and checking report
  4. Versioned companion, source and verification receipts
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