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

TL;DR

This paper proposes infinitely many new renormalization group flows between Virasoro minimal models, induced by non-invertible symmetries, expanding the understanding of these flows beyond previously known cases.

Contribution

It introduces a broad class of new RG flows between Virasoro minimal models based on non-invertible symmetries, generalizing prior specific examples.

Findings

Infinite new RG flows between Virasoro minimal models.

Flows preserve a modular tensor category with SU(2)_{q-2} fusion ring.

Unified framework encompasses previously known sporadic flows.

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 $\phi_{(1,2k+1)}$. They vastly generalize the previously proposed ones $k=I=1$ by Zamolodchikov, $k=1, I>1$ by Ahn and L\"assig, 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.