Non-invertible symmetries in $S_N$ orbifold CFTs and holography

Abstract

We study non-invertible defects in two-dimensional $S_N$ orbifold CFTs. We construct universal defects which do not depend on the details of the seed CFT and hence exist in any orbifold CFT. Additionally, we investigate non-universal defects arising from the topological defects of the seed CFT. We argue that there exist universal defects that are non-trivial in the large-$N$ limit, making them relevant for the AdS${}_3$/CFT${}_2$ correspondence. We then focus on AdS${}_3\times$S${}^3\times {\mathcal{M}}_4$ with one unit of NS-NS flux and propose an explicit realization of these defects on the worldsheet.