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 infnitely many new renormalization group flows between Virasoro minimal models 𝓜(kq + I, q) →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. 𝓜(10, 3) → 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.