Minimal Models RG flows: non-invertible symmetries & non-perturbative description

Abstract

In this letter we continue the investigation of RG flows between minimal models that are protected by non-invertible symmetries. RG flows leaving unbroken a subcategory of non-invertible symmetries are associated with anomaly-matching conditions that we employ systematically to map the space of flows between Virasoro Minimal models beyond the ${\mathbb{Z}}_2$-symmetric proposed recently in the literature. We introduce a family of non-linear integral equations that appear to encode the exact finite-size, ground-state energies of these flows, including non-integrable cases, such as the recently proposed $\mathcal{M}(kq+I,q)\to \mathcal{M}(kq-I,q)$. Our family of NLIEs encompasses and generalises the integrable flows known in the literature: ${\varphi }_{(1,3)}$, ${\varphi }_{(1,5)}$, ${\varphi }_{(1,2)}$ and ${\varphi }_{(2,1)}$. This work uncovers a new interplay between exact solvability and non-invertible symmetries. Furthermore, our non-perturbative description provides a non-trivial test for all the flows conjectured by anomaly matching conditions, but so far not-observed by other means.

6 pages + Supplemental materials; v3: Published version in PRL

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