Symmetry enhancement in RCFT II

TL;DR

The paper extends symmetry-enhancement analyses from bosonic to fermionic RCFTs by leveraging RG invariants within braided fusion categories and a striking UV–IR double braiding relation. It shows that while F-symbols are rigid, braidings can jump at fixed points, yielding strong constraints on RG flows and enabling predictions of IR conformal data. The authors propose a criterion based on Γ_θ-BFCs that governs when symmetry enhancement must occur in NS-NS spin structure, and demonstrate this through detailed testing on fermionic minimal models, where double braiding data together with monotonicity fixes IR dimensions and clarifies the structure of the theory space. These results provide a robust framework for understanding emergent symmetries and massless flows in fermionic RCFTs, with potential applicability to higher-dimensional non-invertible symmetries.

Abstract

We explain when and why symmetries enhance in fermionic rational conformal field theories. In order to achieve the goal, we first clarify invariants under renormalization group flows. In particular, we find the Ocneanu rigidity is not enough to protect some quantities. Concretely, while (double) braidings are subject to the rigidity, they jump at conformal fixed points. The jump happens in a specific way, so the double braiding relation further constrains renormalization group flows. The new constraints enable us three things; 1) to predict infrared conformal dimensions in massless flow, 2) to reveal some structures of the theory space, and 3) to obtain a necessary condition for a flow to be massless. We also find scaling dimensions ``monotonically'' decrease along massless flows. Combining the discovery with predictions, sometimes, we can uniquely fix infrared conformal dimensions.