Higher categorical symmetries and gauging in two-dimensional spin systems

Understand

We present a framework to systematically investigate higher categorical symmetries in two-dimensional spin systems.

• Though exotic, such generalised symmetries have been shown to naturally arise as dual symmetries upon gauging invertible symmetries.
• Our framework relies on an approach to dualities whereby dual quantum lattice models only differ in a choice of module 2-category over some input fusion 2-category.
• Given an arbitrary two-dimensional spin system with an ordinary symmetry, we explain how to perform the (twisted) gauging of any of its sub-symmetries.