Flux Quantization

Hisham Sati, Urs Schreiber
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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.
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通量量化
麦克斯韦类型的高规场--例如普通电磁场("A场"),以及弦/M理论中考虑的B场、RR场和C场--的通量和电荷量化定律通过编码这些场的孤子行为,从而通过指定场通量来源的单个支链(高维单极子或孤子)所携带的离散电荷,来指定这些场的非微扰完备性。这篇文章探讨了一般(有理)同调理论对通量和电荷量化的理解,通量和电荷量化通过切尔诺-多尔德特性图泛化到非线性(自源)比安奇特性,这些特性出现在高维超引力理论中,特别是 D=10 的 B&RR 场、D=11 超引力中的 C 场和五布兰世界卷上的 B 场。
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