Complete Topological Quantization of Higher Gauge Fields

TL;DR

This paper develops a comprehensive topological quantization framework for higher gauge fields, linking flux quantization in nonabelian cohomology to quantum observables and states in supergravity and M-theory contexts.

Contribution

It introduces a novel flux quantization approach in extraordinary nonabelian cohomology that fully determines topological quantum states and observables in higher gauge theories.

Findings

Flux quantization in Cohomotopy recovers abelian Chern-Simons observables.

The framework predicts anyons in fractional quantum Hall systems.

Global completion hypotheses relate to M-theory and M5-branes.

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.