I'm (vaguely) aware of certain uses of higher category theory in attempts to mathematically understand quantum field theories -- for example, Lurie's work on eTQFTs, the recent-ish book by Paugam, and a bunch of work by people like Urs Schreiber.

What I'm wondering is: what work has been done at understanding the role of renormalization in quantum field theory in these terms (specifically in terms of homotoptic geoemtry or something along those lines)? And since much of the work I've seen along these lines tends to focus on perturbative QFT (with good reason, of course), are there are good references which try to capture the non-perturbative aspects of QFT from this perspective?

This post imported from StackExchange Physics at 2016-10-18 13:58 (UTC), posted by SE-user OperaticDreamland