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

TL;DR

This paper investigates RG flows between minimal models protected by non-invertible symmetries, introducing a family of non-linear integral equations to describe these flows non-perturbatively, including non-integrable cases, and testing conjectured flows.

Contribution

It introduces a new family of non-linear integral equations that encode exact finite-size energies for RG flows with non-invertible symmetries, extending known integrable cases.

Findings

Unified description of integrable and non-integrable flows

Non-perturbative testing of anomaly-matching conjectures

New insights into the role of non-invertible symmetries in RG flows

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 $\mathcal{M}(k q + I,q) \to \mathcal{M}(k q - I,q)$. Our family of NLIEs encompasses and generalises the integrable flows known in the literature: $\phi_{(1,3)}$, $\phi_{(1,5)}$, $\phi_{(1,2)}$ and $\phi_{(2,1)}$. 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.