标题： M5-膜上的磁通量量子化 显示英文标题

标题： Flux Quantization on M5-branes

摘要： M5膜被认为可能为强耦合量子系统中的各种非微扰现象提供急需的理论基础，然而其经典层场公式中已经存在的主要非微扰效应却很少受到关注：即其世界体积上的高阶规范场的流量化。 由于（1a.）小场极限下3形式通量密度的著名自对偶性，以及（1b.）强场下的高度非线性自对偶性，这一问题显得微妙，并且（2a.）其Bianchi恒等式被11维超引力C场通量密度的拉回所扭曲，这（2b.）本身受制于其在环境时空中的微妙通量量子化定律。 这些微妙之处质疑了隐含假设，即M5膜的3通量在普通上同调中被量子化，因此留下了关于M5膜的世界体积高阶规范场究竟是什么这样一个相当基本的问题。 在这里，我们在（非阿贝尔）广义扭转变分上同调中表征了M5膜3通量的有效量子化定律。 关键步骤是转到超时空，并在那里将特征映射与层场M5膜场的“超嵌入”构造相结合，我们给出了一个严格且简洁的重新推导。 我们证明了M5膜上3通量的一个可接受的量子化定律是由“假设H”预测的4-同伦扭变3-同伦扭变。 除了量化体通量（G4,G7）和膜自身的H3通量外，该定律还意味着诱导的Page电荷/Hopf-WZ项在M5膜上的（能级）量子化，这对于使其作用泛函全局良好定义是必要的。 最后，我们展示了如何在这种通量量子化条件下，M5膜上通常会出现涡旋孤立子，而开放M5膜上则会出现任意子拓扑量子态。 显示英文摘要

摘要： The M5-brane has been argued to potentially provide much-needed theoretical underpinning for various non-perturbative phenomena in strongly-coupled quantum systems and yet the primary non-perturbative effect already in its classical on-shell formulation has received little attention: The flux-quantization of the higher gauge field on its worldvolume. This problem appears subtle because of (1a.) the notorious self-duality of the 3-form flux density in the small field limit, combined with (1b.) its highly non-linear self-duality for strong fields, and (2a.) the twisting of its Bianchi identity by the pullback of the 11d SuGra C-field flux density, which (2b.) is subject to its own subtle flux quantization law on the ambient spacetime. These subtleties call into question the tacit assumption that the M5 brane's 3-flux is quantized in ordinary cohomology and hence leaves open the rather fundamental question of what the M5-brane's worldvolume higher gauge field really is. Here we characterize the valid quantization laws of the M5-brane's 3-flux in (non-abelian) generalized twisted cohomology. The key step is to pass to super-spacetime and there to combine the character map with the "super-embedding"-construction of the on-shell M5-brane fields, of which we give a rigorous and streamlined re-rederivation. We show that one admissible quantization law of the 3-flux on M5-branes is by 4-Cohomotopy-twisted 3-Cohomotopy, as predicted by "Hypothesis H". Besides quantizing the bulk fluxes (G4,G7) and the brane's H3-flux themselves, this law also implies the (level-)quantization of the induced Page-charge/Hopf-WZ term on the M5-brane, necessary for its action functional to be globally well-defined. Finally, we demonstrate how with this flux quantization imposed, there generically appear skyrmionic solitons on M5-branes and anyonic topological quantum states on open M5-branes.