We study in general spacetime dimension the symmetry of the theory obtained by gauging a
non-anomalous finite normal Abelian subgroup $ A $ of a $\Gamma $-symmetric theory …

A bstract We discuss the fermionization of fusion category symmetries in two-dimensional
topological quantum field theories (TQFTs). When the symmetry of a bosonic TQFT is …

A bstract We construct topological quantum field theories (TQFTs) and commuting projector
Hamiltonians for any 1+ 1d gapped phases with non-anomalous fusion category …

Fracton phases exhibit striking behavior which appears to render them beyond the standard
topological quantum field theory (TQFT) paradigm for classifying gapped quantum matter …

group symmetries arise when 1-form symmetries and 0-form symmetries of a theory mix with
each other under group multiplication. We discover the existence of 2-group symmetries in …

We uncover 2-group symmetries in 6d superconformal field theories. These symmetries
arise when the discrete 1-form symmetry and continuous flavor symmetry group of a theory …

This is a survey article for the Encyclopedia of Mathematical Physics, 2nd Edition.
Topological defects are described in the context of the 2-dimensional Ising model on the …

We introduce the notion of n–dimensional topological quantum field theory (TQFT) with
defects as a symmetric monoidal functor on decorated stratified bordisms of dimension n …

We present commuting projector Hamiltonian realizations of a large class of (3+ 1) D
topological models based on mathematical objects called unitary G-crossed braided fusion …

We develop a general theory of 3-dimensional``orbifold completion'', to describe
(generalised) orbifolds of topological quantum field theories as well as all their defects …