Flux Quantization

TL;DR

This paper explores the mathematical framework behind flux and charge quantization in higher gauge fields relevant to string and M-theory, emphasizing non-perturbative aspects and solitonic behaviors.

Contribution

It provides a homotopy-theoretic perspective on flux and charge quantization, extending the Chern-Dold character to nonlinear Bianchi identities in supergravity theories.

Findings

Unified understanding of flux quantization in various supergravity fields

Application of rational homotopy theory to non-perturbative fluxes

Generalization of the Chern-Dold character to nonlinear identities

Abstract

Flux- and charge-quantization laws for higher gauge fields of Maxwell type -- e.g. the common electromagnetic field (the "A-field") but also the B-, RR-, and C-fields considered in string/M-theory -- specify non-perturbative completions of these fields by encoding their solitonic behaviour and hence by specifying the discrete charges carried by the individual branes (higher-dimensional monopoles or solitons) that source the field fluxes. This article surveys the general (rational-)homotopy theoretic understanding of flux- and charge-quantization via the Chern-Dold character map generalized to the non-linear (self-sourcing) Bianchi identities that appear in higher-dimensional supergravity theories, notably for B&RR-fields in D=10, for the C-field in D=11 supergravity, and for the B-field on fivebrane worldvolumes.