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arXiv · 2601.18667

RG flows of minimal $\mathcal W$-algebra CFTs via non-invertible symmetries

Federico Ambrosino·Tomáš Procházka
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Abstract

In this letter we study renormalization group (RG) flows between 2d conformal field theories enjoying extended higher-spin $\mathcal{W}$-symmetry. We propose a new class of RG flows between the diagonal minimal models of $\mathcal{W}_N$-algebra that take the form $\mathcal{W}_N(p,q)\to\mathcal{W}_N(p,kp-q)$. These are obtained by matching the anomalies of the non-invertible symmetry ${\mathrm{Rep}}[SU(N)_{p-N}]$ (and its discrete quotients) that is preserved by special relevant primary fields. This large non-invertible symmetry includes the familiar $\mathbb{Z}_N$ symmetry of the minimal models. Our new flows furnish a significant generalization of the ones recently found in the case of Virasoro algebra, and include all previously known RG flows of $\mathcal{W}_N$. They have the remarkable property of being uniform in the rank $N$ of the $\mathcal{W}$-algebra.

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Federico Ambrosino, Tomáš Procházka. 2026-01-26. RG flows of minimal $\mathcal W$-algebra CFTs via non-invertible symmetries. https://arxiv.org/abs/2601.18667

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