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

TL;DR

This paper explores non-invertible defects in two-dimensional $S_N$ orbifold conformal field theories, constructing universal defects independent of seed CFT details and analyzing their implications for holography and the AdS$_3$/CFT$_2$ correspondence.

Contribution

It introduces universal non-invertible defects in $S_N$ orbifold CFTs that are relevant in the large-$N$ limit and provides an explicit worldsheet realization in AdS$_3$ backgrounds.

Findings

Universal defects exist in any orbifold CFT.

Universal defects are non-trivial in the large-$N$ limit.

Explicit realization of defects in AdS$_3$ string theory.

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.