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) → \( \mathcal{M} \) (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 ℤ2 preserving renormalization group flows sporadically known in the literature (e.g. \( \mathcal{M} \) (10, 3) → \( \mathcal{M} \) (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.
