Construct the BDI-to-D holographic theory

Construct a holographic theory relating one-dimensional class-BDI topological quantum critical points to a suitable higher-dimensional gapped class-D bulk while accounting for the nonchiral nature of the one-dimensional critical boundary.

Background

The Bott-clock construction encounters a dimensional and chirality mismatch when connecting class BDI to class D. The one-dimensional BDI critical point is nonchiral, whereas the boundary of a two-dimensional class-D superconductor is chiral, so the paper does not complete this connection in the main text and refers to an appendix for a related construction using emergent symmetries.

References

However, the boundary states of class D superconductors in 2D are always chiral but the 1D tQCP is nonchiral. Therefore, we are not able to construct a holographic theory between class BDI tQCPs in 1D and gapped class D bulk in 2D.

— Holographic Representations of Topological Quantum Criticality: Emergent Symmetry Approach around the Bott Clock  (2608.30335 - Yang et al., 31 Aug 2026) in Section 3, subsection “From BDI to D” (Section \ref{sec:closure})