We identify infinitely many noninvertible generalized global symmetries in QED and QCD for
the real world in the massless limit. In QED, while there is no conserved Noether current for …

We discuss a variety of codimension-one, non-invertible topological defects in general 3+ 1d
QFTs with a discrete one-form global symmetry. These include condensation defects from …

In gauge theory, it is commonly stated that time-reversal symmetry only exists at θ= 0 or π for
a 2 π-periodic θ angle. In this Letter, we point out that in both the free Maxwell theory and …

We survey recent developments in a novel kind of generalized global symmetry, the non-
invertible symmetry, in diverse spacetime dimensions. We start with several different but …

Non-Abelian optics has emerged as a promising research field with the potential to
revolutionize our understanding of light–matter interactions and enable new applications in …

We examine the interplay of symmetry and topological order in 2+ 1-dimensional topological
quantum phases of matter. We present a precise definition of the topological symmetry …

We present designs for scalable quantum computers composed of qubits encoded in
aggregates of four or more Majorana zero modes, realized at the ends of topological …

Solitonic symmetry has been believed to follow the homotopy-group classification of
topological solitons. Here, we point out a more sophisticated algebraic structure when …

We study 3d and 4d systems with a one-form global symmetry, explore their consequences,
and analyze their gauging. For simplicity, we focus on $\mathbb {Z} _N $ one-form …

The phenomenon of fractional quantum Hall effect (FQHE) was first experimentally observed
33 years ago. FQHE involves strong Coulomb interactions and correlations among the …