Existence of a symmetric trivial gapped interface between free-fermion and commuting-projector SPTs

Establish the existence and explicitly construct a symmetric, topologically trivial gapped interface between a free‑fermion symmetry‑protected topological slab and a commuting‑projector symmetry‑protected topological slab (with the same U(1)_V × U(1)_A topological response), as required for the in‑flow construction to produce a chiral theory while preserving the symmetry on the lattice.

Background

The authors present an in‑flow formulation in which a (D+1)-dimensional commuting‑projector SPT slab is coupled to a free‑fermion SPT slab, aiming to realize chiral boundary modes while maintaining on‑site symmetry in the bulk. This requires a symmetric, topologically trivial gapped interface between the two slabs.

They argue the interface should exist if both models represent the same SPT phase, based on matching Chern–Simons responses; however, they explicitly state that the existence of such an interface is a plausible but unproven conjecture, marking it as an open problem central to validating the proposed construction.