Complete Topological Quantization of Higher Gauge Fields
Abstract
After global completion of higher gauge fields (as appearing in higher-dimensional supergravity) by proper flux quantization in extraordinary nonabelian cohomology, the (non-perturbative, renormalized) topological quantum observables and quantum states of solitonic field histories are completely determined through a topological form of light-front quantization. We survey the logic of this construction and expand on aspects of the quantization argument. In the instructive example of 5D Maxwell-Chern-Simons theory (the gauge sector of 5D SuGra) dimensionally reduced to 3D, a suitable choice of flux quantization in Cohomotopy ("Hypothesis h") recovers this way the fine detail of the traditionally renormalized (Wilson loop) quantum observables of abelian Chern-Simons theory and makes novel predictions about anyons in fractional quantum (anomalous) Hall systems. An analogous choice ("Hypothesis H") of global completion of 11D higher Maxwell-Chern-Simons theory (the higher gauge sector of 11D SuGra) realizes various aspects of the topological sector of the conjectural "M-theory" and its M5-branes.
Cite
@article{arxiv.2512.12431,
title = {Complete Topological Quantization of Higher Gauge Fields},
author = {Hisham Sati and Urs Schreiber},
journal= {arXiv preprint arXiv:2512.12431},
year = {2026}
}
Comments
55 amsart pages + references, 11 figures; these are expanded lecture notes for the mini-course of the same title held at ICMS Edinburgh, Dec. 2025; v2: new Ex. 1.18 added, minor polishing, for publication with SciPost Physics