Continuous symmetric mass generation for sixteen Weyl fermions in 4D
In plain words
Particles normally get mass by breaking a symmetry. The question is whether strong interactions can give mass to sixteen massless fermions in four dimensions while every symmetry is kept, through a smooth (continuous) change from the massless phase.
Precise statement
For 16 Weyl fermions in 4D (one Standard Model generation with a right-handed neutrino) with interactions preserving Spin(10) or a subgroup with vanishing 't Hooft anomalies, a lattice model may have a gapped phase with no symmetry breaking, no topological order and vanishing bilinear condensates. Determine whether such a phase is reached from the massless phase by a direct continuous transition, which is what a continuum symmetric-mass-generation theory requires.
What would settle it
Lattice Monte Carlo of a 4D staggered or domain-wall model showing a direct continuous transition from the massless phase to a gapped phase with unbroken symmetry and no Goldstone modes, or a proof that an intermediate phase is unavoidable.
Status in the literature
Unverified note
Staggered-fermion lattice studies (Butt, Catterall, Hasenfratz and collaborators, 2021-2026) find a massive symmetric phase in 4D; a 2024 gauge-theory study reports a continuous transition, while a 2026 four-fermion study finds the massless and massive symmetric phases separated by an intermediate antiferromagnetic phase.