For a zero-temperature Landau symmetry-breaking transition in n-dimensional space that
completely breaks a finite symmetry G, the critical point at the transition has the symmetry G …

A global symmetry (0-symmetry) in an n-dimensional space acts on the whole space. A
higher symmetry acts on closed submanifolds (ie, loops and membranes, etc.), and those …

Although it has been a well-known fact, for more than two decades, that category theory is
needed for the study of topological orders, it is still a non-trivial challenge for students and …

A bstract We consider exactly solvable models in (3+ 1) d whose ground states are
described by topological lattice gauge theories. Using simplicial arguments, we emphasize …

This is an invited survey article on higher gauge theory for the Encyclopedia of Mathematical
Physics, 2nd edition. In particular, we provide a lightning introduction to higher structures …

We consider compact U κ (1) gauge theory in 3+ 1 dimensions with a general 2 π-quantized
topological term∑ I, J= 1 κ KIJ 4 π∫ M 4 FI∧ FJ, where K is an integer symmetric matrix with …

A bstract We explore 2-form topological gauge theories in (3+ 1) d. These theories can be
constructed as sigma models with target space the second classifying space B 2 G of the …

We propose a bosonic U κ (1) rotor model on a three dimensional spacetime lattice. With the
inclusion of a Maxwell term, we show that the low-energy properties of our model can be …

While winding a particlelike excitation around a looplike excitation yields the celebrated
Aharonov-Bohm phase, we find a distinctive braiding phase in the absence of such mutual …

A bstract We consider lattice Hamiltonian realizations of (d+ 1)-dimensional Dijkgraaf-Witten
theory. In (2+ 1) d, it is well-known that the Hamiltonian yields point-like excita-tions …