Defect Conformal Manifolds along RG Domain Walls between $\mathbb Z_N$-Parafermions and Minimal Models
Abstract
We investigate the renormalization group (RG) domain walls interpolating between the parafermion theory (the critical -state Potts model) and the Virasoro minimal model . These flows are genuinely non-perturbative and an explicit construction of Gaiotto type RG domain wall remains elusive. We bypass this limitation by employing a bottom-up approach centered on the emergence of ``phantom currents". By tracking the preserved non-invertible symmetries () along the flow, we extract the exact spectrum of these currents localized on the defect. We demonstrate that the presence of a spin-1 phantom current allows the interface to be marginally deformed, dynamically generating a continuous defect conformal manifold. Furthermore, we show that an extra spin-2 operator, crucially as a -algebra descendant of the spin-1 phantom current, rigidly constrains the UV-IR stress tensor mixing via the cluster decomposition principle. This algebraic framework enables the exact computation of the parameter-dependent transmission rate across the conformal manifold, which we observe strictly vanishes in the large- limit as a consequence of macroscopic target space collapse.
Keywords
Cite
@article{arxiv.2605.24978,
title = {Defect Conformal Manifolds along RG Domain Walls between $\mathbb Z_N$-Parafermions and Minimal Models},
author = {Jin-Rui Zhang and Jing-Hao Jin and Ting-Kai Chen and Jin Chen},
journal= {arXiv preprint arXiv:2605.24978},
year = {2026}
}
Comments
23 pages plus 4 appendices