2025/12/13 by Sati, Hisham, Schreiber, Urs
#18G35 #53C08 #55N20 #55P62 #81T30 #81T35 #81T45 81T13 #81V27 #81V70 #Algebraic Topology (math.AT) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Primary: 81T70 #Quantum Physics (quant-ph) #Secondary: 83E50 #Strongly Correlated Electrons (cond-mat.str-el)
paper · doi:10.48550/arxiv.2512.12431
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.