Symmetry enhancement in RCFT

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.

11 pages + Appendices; v2: reference and comment added; v3: added explicit comment on "naturalness," and fixed typo; v4: fixed braiding matrices and typos, results unchanged, a reference added; v5: fixed identifications of TDLs, results unchanged

References in corpus (9)

• Generalized Global Symmetries
• Duality and defects in rational conformal field theory
• Fusion Category Symmetry I: Anomaly In-Flow and Gapped Phases
• Fusion Category Symmetry II: Categoriosities at c = 1 and Beyond
• Anomaly Obstructions to Symmetry Preserving Gapped Phases
• Lorentzian Dynamics and Factorization Beyond Rationality
• Some Exact Results in QCD-like Theories
• Symmetry enhancement in 4d Spin(n) gauge theories and compactification from 6d
• Modular Categories

Cited by in corpus (6)

• Construction of two-dimensional topological field theories with non-invertible symmetries
• Fusion Surface Models: 2+1d Lattice Models from Fusion 2-Categories
• Topological Defect Lines in Two Dimensional Fermionic CFTs
• Fermionic Non-Invertible Symmetries in (1+1)d: Gapped and Gapless Phases, Transitions, and Symmetry TFTs
• Hecke Relations, Cosets and the Classification of 2d RCFTs
• Anyon condensation in mixed-state topological order