Symmetry enhancement in RCFT

TL;DR

The paper investigates when and why symmetry enhancements occur in massless RG flows to 2D RCFTs, focusing on unitary minimal models perturbed by $igl( angle ext{phi}_{1,3}igr)$. It proposes that IR symmetry data must form a modular tensor category (MTC) compatible with the $c$-theorem; if the surviving category is non-modular or violates $c$-theorem constraints, emergent topological defect lines enlarge it to an appropriate MTC. Through detailed analysis of flows from $M(m+1,m)$ to $M(m,m-1)$, it shows that odd $m$ requires symmetry enhancement while even $m$ does not, with explicit examples for $m=4,5,6$ illustrating how emergent lines reconcile UV and IR data and, in some cases, imply higher-rank MTCs. The work thus links RG flow, Verlinde lines, and categorical modularity to predict symmetry enhancements and inform MTC classifications in RCFTs.

Abstract

We propose when and why symmetry enhancements happen in massless renormalization group (RG) flows to two-dimensional rational conformal field theories (RCFTs). We test our proposal against known RG flows from unitary minimal models. We also suggest which sign of the relevant coupling triggers the massless RG flow. The other sign triggers massive RG flows to topological quantum field theories (TQFTs). We comment on their ground state degeneracies.