We show that the standard 1+ 1 DZ 2× Z 2 cluster model has a noninvertible global
symmetry, described by the fusion category Rep (D 8). Therefore, the cluster state is not only …

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 …

A bstract Gauging is a powerful operation on symmetries in quantum field theory (QFT), as it
connects distinct theories and also reveals hidden structures in a given theory. We initiate a …

A bstract Symmetry is a powerful tool for studying dynamics in QFT: it provides selection
rules, constrains RG flows, and often simplifies analysis. Currently, our understanding is that …

We discuss the exact non-invertible Kramers-Wannier symmetry of 1+ 1d lattice models on a
tensor product Hilbert space of qubits. This symmetry is associated with a topological defect …

We derive model-independent quantization conditions on the axion couplings (sometimes
known as the anomaly coefficients) to the standard model gauge group [SU (3)× SU (2)× U …

The classification and characterization of topological phases of matter is well understood for
ground states of gapped Hamiltonians that are well isolated from the environment. However …

A bstract We discuss two-dimensional conformal field theories (CFTs) which are invariant
under gauging a non-invertible global symmetry. At every point on the orbifold branch of c …

The global symmetries of a D-dimensional quantum field theory (QFT) can, in many cases,
be captured in terms of a (D+ 1)-dimensional symmetry topological field theory (SymTFT). In …

We study the holographic dual of a topological symmetry operator in the context of the
AdS/CFT correspondence. Symmetry operators arise from topological field theories …