In the context of string theory I recently read "The formulation of Chern-Simons theory in terms of monodromy defects can be carried through all the dualities of the present paper, leading to descriptions based on codimension two defects in various dimensions, as we explain briefly in section 6. This matter certainly merits much closer attention."

Can somebody explain what monodromy defects are?

[Edit: The quoted sentence appears in the introduction of this arxiv preprint of Ed Witten. --PLC]