Consistency of the Grabowska–Kaplan and Disk Frameworks in the Continuum Limit

Determine whether the five-dimensional Grabowska–Kaplan slab framework and the Kaplan–Sen disk framework yield a consistent four-dimensional quantum field theory in the continuum limit. Ascertain this for their intended applications to chiral gauge theories and QCD, given that these constructions possess an exact, gauge-invariant conserved current that is not present in the target continuum theories.

Background

The paper analyzes two five-dimensional proposals—the Grabowska–Kaplan slab framework and the Kaplan–Sen disk framework—designed to construct lattice chiral gauge theories while maintaining gauge invariance. The authors show that both constructions inevitably contain a conserved and gauge-invariant current (the total fermion number in chiral theories or the singlet axial current in vector-like theories) that should be anomalous in the target four-dimensional theory.

Because this exact symmetry leads to a superfluous Nambu–Goldstone boson (e.g., a singlet pseudoscalar in QCD) if chiral symmetry breaks, the authors raise concerns about universality. They explicitly note that it remains an open question whether these proposals can produce a consistent four-dimensional quantum field theory in the continuum limit, or whether they necessarily define a different universality class from standard QCD and chiral gauge theories.