2024/12/12 by Ken Kikuchi, Kikuchi, Ken · 4 citations
Mathematics · #Advanced Topology and Set Theory #Category Theory (math.CT) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Quantum Algebra (math.QA) #Strongly Correlated Electrons (cond-mat.str-el)
paper · pdf · doi:10.48550/arxiv.2412.08935
openalex publication_date 2024/12/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Consider a renormalization group flow preserving a pre-modular fusion category \mathcal S1. If it flows to a rational conformal field theory, the surviving symmetry \mathcal S1 flows to a pre-modular fusion category \mathcal S2 with monoidal functor F:\mathcal S1→\mathcal S2. By clarifying mathematical (especially category theoretical) meaning of renormalization group domain wall/interface or boundary condition, we find the hidden extended vertex operator (super)algebra gives a unique (up to braided equivalence) completely (\mathcal S1\boxtimes\mathcal S2)'-anisotropic representative of the Witt equivalence class [\mathcal S1\boxtimes\mathcal S2]. The mathematical conjecture is supported physically, and passes various tests in concrete examples including non/unitary minimal models, and Wess-Zumino-Witten models. In particular, the conjecture holds beyond diagonal cosets. The picture also establishes the conjectured half-integer condition, which fixes infrared conformal dimensions mod \frac12. It further leads to the double braiding relation, namely braiding structures jump at conformal fixed points. As an application, we solve the flow from the E-type minimal model (A10,E6)→ M(4,3).