Topological operators, noninvertible symmetries and decomposition

Understand

In this paper we discuss the relationship between noninvertible topological operators, one-form symmetries, and decomposition of two-dimensional quantum field theories, focusing on two-dimensional orbifolds with and without discrete torsion.

• As one component of our analysis, we study the ring of dimension-zero operators in two-dimensional theories exhibiting decomposition.
• From a commutative algebra perspective, the rings are naturally associated to a finite number of points, one point for each universe in the decomposition.
• Each universe is canonically associated to a representation, which defines a projector, an idempotent in the ring of dimension-zero operators.