Infinitely many new renormalization group flows between Virasoro minimal models from non-invertible symmetries

Abstract

Abstract Based on the study of non-invertible symmetries, we propose there exist infinitely many new renormalization group flows between Virasoro minimal models M $$ \mathcal{M} $$ (kq + I, q) → M $$ \mathcal{M} $$ (kq – I, q) induced by ϕ (1,2k+1). They vastly generalize the previously proposed ones k = I = 1 by Zamolodchikov, k = 1, I > 1 by Ahn and Lässig, and k = 2 by Dorey et al. All the other ℤ 2 preserving renormalization group flows sporadically known in the literature (e.g. M $$ \mathcal{M} $$ (10, 3) → M $$ \mathcal{M} $$ (8, 3) studied by Klebanov et al) fall into our proposal (e.g. k = 3, I = 1). We claim our new flows give a complete understanding of the renormalization group flows between Virasoro minimal models that preserve a modular tensor category with the SU(2) q−2 fusion ring.

Keywords

• Field Theories in Lower Dimensions
• Global Symmetries
• Renormalization Group
• Scale and Conformal Symmetries