Schreiber Renormalization of Wilson Loops

An article that we have written at CQTS:

---

• Hisham Sati$\;\;\;$and$\;\;\;$ Urs Schreiber:

  
  

  Renormalization of Wilson Loop Observables via

  Proper Flux Quantization in Cohomotopy

  
  

  Reviews in Mathematical Physics (2026)

  doi:10.1142/S0129055X25500382

  
  

  • main article:

    • pdf, arXiv:2509.25336

  • extended abstract for Oberwolfach Reports:

    • pdf @ doi:10.4171/OWR/2025/44

  • video invitation:

    • YT

  
  

• following a presentation at:

  
  

  Oberwolfach Mini-Workshop 2539b:

  Renormalization and Randomness (mfo:4362, program: pdf)

  Mathematical Research Institute Oberwolfach (MFO)

  21-26 Sep 2025

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 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 proper flux quantization in 4-Cohomotopy (“Hypothesis H”).

---

Based on:

• Cohomotopy, Framed Links, and Abelian Anyons

• Fractional Quantum Hall Anyons via the Algebraic Topology of exotic Flux Quanta

Related presentations:

• Rethinking FQH Anyons (talk)

• Rethinking Topological Quantum (lightning talk)

• Non-Lagrangian construction of FQH Anyons via Flux Quantization in 2-Cohomotopy (proceedings)

• Complete Topological Quantization of Higher (SuGra-type) Gauge Fields

Followup articles:

• Orientations of Orbi-K-Theory measuring Topological Phases and Brane Charges