Quantum many-body systems with a non-Abelian topological order can host anyonic
quasiparticles. It has been proposed that anyons could be used to encode and manipulate …

We propose a general framework to characterize gapped infra-red (IR) phases of theories
with non-invertible (or categorical) symmetries. In this paper we focus on (1+ 1) d gapped …

We derive a refined version of the Affleck-Ludwig-Cardy formula for a 1+ 1 D conformal field
theory, which controls the asymptotic density of high energy states on an interval …

What does it mean for a boundary condition to be symmetric with respect to a noninvertible
global symmetry? We discuss two possible definitions in 1+ 1 D QFTs and lattice models. On …

A bstract In this paper we discuss gauging noninvertible zero-form symmetries in two
dimensions. We specialize to certain gaugeable cases, specifically, fusion categories of the …

We present a systematic recipe for generating and classifying duality transformations in one-
dimensional quantum lattice systems. Our construction emphasizes the role of global …

A bstract We consider the triality fusion category discovered in the c= 1 Kosterlitz-Thouless
theory [1]. We analyze this fusion category using the tools from the group theoretical fusion …

We introduce a class of generalized tube algebras which describe how finite, non-invertible
global symmetries of bosonic 1+ 1d QFTs act on operators which sit at the intersection point …

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 …

Topological quantum error correction based on the manipulation of the anyonic defects
constitutes one of the most promising frameworks towards realizing fault-tolerant quantum …