Renormalization of Chern-Simons Wilson Loops via Flux Quantization in Cohomotopy

Abstract

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. 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 flux quantization of 11D supergravity in 4-Cohomotopy ("Hypothesis H").

arXiv comment35 pages, 11 figures; expanded account of results presented at Oberwolfach Mini-Workshop 2539b: "Renormalization and Randomness"; v2: paragraphs on the 2d TQFT picture added