Renormalization of Chern–Simons Wilson loops via proper flux quantization in cohomotopy

In the practice of physics model building, the process of renormalization, resummation, and anomaly cancellation is to incrementally repair initially ill-defined Lagrangian quantum field theories by a successive choice of partial fixes. Impressive as this is, one would rather have concisely defined complete theories to begin with, and understand these choices as emergent from fundamental principles. As an instructive example, we recall renormalization choices for Wilson loop observables in abelian Chern–Simons theory. Then we show that these emerge in a novel non-Lagrangian topological completion of 5D Maxwell–Chern–Simons QFT, by means of proper flux quantization in 2-Cohomotopy. This result is a modest cousin, with applications to topologically ordered quantum materials, of the more ambitious completion of 11D supergravity by flux quantization in 4-Cohomotopy (“Hypothesis H”).