Two-dimensional algebra in lattice gauge theory

Understand

We provide a visual and intuitive introduction to effectively calculating in 2-groups along with explicit examples coming from non-abelian 1- and 2-form gauge theory.

• In particular, we utilize string diagrams, tools similar to tensor networks, to compute the parallel transport along a surface using approximations on a lattice.
• Although this work is mainly intended as expository, we prove a convergence theorem for the surface transport in the continuum limit.
• Locality is used to define infinitesimal parallel transport and two- dimensional algebra is used to derive finite versions along arbitrary surfaces with sufficient orientation data.