Categorical Symmetries at Criticality

Understand

We study the concept of "categorical symmetry" introduced recently, which in the most basic sense refers to a pair of dual symmetries, such as the Ising symmetries of the $1d$ quantum Ising model and its self-dual counterpart.

• In this manuscript we study discrete categorical symmetry at higher dimensional critical points and gapless phases.
• At these selected gapless states of matter, we can evaluate the behavior of categorical symmetries analytically.
• We analyze the categorical symmetry at the following examples of criticality: (1) Lifshit critical point of a $(2+1)d$ quantum Ising system; (2) $(3+1)d$ photon phase as an intermediate gapless phase between the topological order and the confined phase of 3d $Z_2$ quantum gauge theory; (3) $2d$ and $3d$ examples of systems with both categorical symmetries (either 0-form or 1-form categorical symmetries) and subsystem symmetries.