Symmetry enhancement in RCFT II

TL;DR

This paper investigates symmetry enhancement in fermionic rational conformal field theories, revealing how certain invariants change under renormalization group flows and enabling predictions of infrared conformal dimensions.

Contribution

It introduces new constraints on RG flows in fermionic RCFTs, clarifies the role of double braidings, and provides tools to predict infrared conformal dimensions and structure of theory space.

Findings

Double braidings jump at conformal fixed points.

Scaling dimensions decrease monotonically along massless flows.

New necessary conditions for flows to be massless.

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.