We introduce a definition and framework for internal topological symmetries in quantum field
theory, including “noninvertible symmetries” and “categorical symmetries”. We outline a …

Is there a vector space whose dimension is the golden ratio? Of course not--the golden ratio
is not an integer! But this can happen for generalizations of vector spaces--objects of a …

Gapped domain walls, as topological line defects between (2+ 1) D topologically ordered
states, are examined. We provide simple criteria to determine the existence of gapped …

We characterize discrete (anti-) unitary symmetries and their non-invertible generalizations
in 2+ 1 d topological quantum field theories (TQFTs) through their actions on line operators …

We develop a systematic theory of symmetry fractionalization for fermionic topological
phases of matter in (2+ 1) D with a general fermionic symmetry group G f. In general, G f is a …

We present an exactly solvable lattice Hamiltonian to realize gapped boundaries of Kitaev's
quantum double models for Dijkgraaf-Witten theories. We classify the elementary excitations …

This paper studies fault-tolerant quantum computation with gapped boundaries. We first
introduce gapped boundaries of Kitaev's quantum double models for Dijkgraaf-Witten …

We study the anomalies of non-invertible symmetries in 1+ 1D QFTs using gapped
boundaries of its SymTFT. We establish the explicit relation between Lagrangian algebras …

The anomaly for the Monster group MM acting on its natural (aka moonshine) representation
V^ ♮ V♮ is a particular cohomology class ω^ ♮ ∈\rm H^ 3 (M,\rm U (1)) ω♮∈ H 3 (M, U (1)) …

We develop a theory of anomalies of fermionic topological phases of matter in (2+ 1) D with
a general fermionic symmetry group G f. In general, G f can be a nontrivial central extension …