2+1D symmetry-topological-order from local symmetric operators in 1+1D

Understand

A generalized symmetry (defined by the algebra of local symmetric operators) can go beyond group or higher group description.

• A theory of generalized symmetry (up to holo-equivalence) was developed in terms of symmetry-TO -- a bosonic topological order (TO) with gappable boundary in one higher dimension.
• We propose a general method to compute the 2+1D symmetry-TO from the local symmetric operators in 1+1D systems.
• Our theory is based on the commutant patch operators, which are extended operators constructed as products and sums of local symmetric operators.