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

TL;DR

This paper investigates new RG flows between 2D conformal field theories with extended $ ext{W}$-symmetry, utilizing non-invertible symmetries to generalize known flows and reveal a uniform structure across different ranks of $ ext{W}_N$-algebras.

Contribution

It introduces a new class of RG flows between minimal $ ext{W}_N$ models based on anomaly matching of non-invertible symmetries, extending previous results and unifying flows across ranks.

Findings

Proposes RG flows of the form $ ext{W}_N(p,q) o ext{W}_N(p,kp-q)$.

Uses anomaly matching of non-invertible symmetries to characterize flows.

Includes all previously known $ ext{W}_N$ RG flows and generalizes them.

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.