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

Abstract

Based on the study of non-invertible symmetries, we propose there exist infinitely many new renormalization group flows between Virasoro minimal models $\mathcal{M}(kq+I,q)\to \mathcal{M}(kq-I,q)$ induced by $\ddot{I}{•}_{(1,2k+1)}$. 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 ${\mathbb{Z}}_2$ preserving renormalization group flows sporadically known in the literature (e.g. $\mathcal{M}(10,3)\to \mathcal{M}(8,3)$ 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.

30 pages, 6 tables, 2 figures, v2: reference added