Gerbe-holonomy for surfaces with defect networks

Understand

We define the sigma-model action for world-sheets with embedded defect networks in the presence of a three-form field strength.

• We derive the defect gluing condition for the sigma-model fields and their derivatives, and use it to distinguish between conformal and topological defects.
• As an example, we treat the WZW model with defects labelled by elements of the centre Z(G) of the target Lie group G; comparing the holonomy for different defect networks gives rise to a 3-cocycle on Z(G).
• Next, we describe the factorisation properties of two-dimensional quantum field theories in the presence of defects and compare the correlators for different defect networks in the quantum WZW model.