Can interactions decouple mirror fermions in lattice chiral theories
In plain words
Grid versions of fermions come with unwanted partner particles of opposite handedness, called mirror fermions. The proposal is to make the mirrors heavy with strong interactions and leave the wanted particles massless.
Precise statement
In mirror-fermion or domain-wall lattice formulations of an anomaly-free chiral theory, add interactions that gap the mirror sector by symmetric mass generation while the target sector stays massless. Determine whether, after weak gauging, the continuum limit is the target chiral gauge theory with no extra massless states and no fermion propagator zeros that act as ghost-like states. Minimal test case: the 2D U(1) 3-4-5-0 model of Wang and Wen.
What would settle it
A lattice computation in the 3-4-5-0 model, then in 4D, showing the gauged mirror sector decouples with a unitary spectrum, or a proof that propagator zeros are unavoidable.
Status in the literature
Unverified note
Golterman and Shamir (2023-2026) argue that symmetric mass generation produces propagator zeros that spoil the gauged theory; numerical tests in 2D continued in 2026.