BPS荷的n-李代数
Lie n-algebras of BPS charges
摘要：
我们发现了更高的代数结构的诺特电流和BPS收费。已知守恒流的等价类构成一个李代数。我们表明，至少对于目标空间的对称性较高的参数化WZW型西格玛模型，这自然升降机的李（p+1）-代数结构的诺特电流本身。应用于超p膜sigma模型的Green-Schwarz型作用泛函，这产生了超对称代数的传统BPS膜电荷扩展的超李（p+1）-代数精化。我们在高等微分几何的一般性中讨论这一点，它也适用于在其世界体积上具有（更高）规范场的膜。应用到M5膜sigma模型，我们恢复和适当的全球化的M-理论超李代数扩展的11维超等距2膜和5膜收费。通过超越无穷小李理论，我们发现这些费用的上同调修正更高的类比熟悉的D-膜费用的修正，因为它们从普通的上同调解除扭曲的K-理论。这支持了M-膜电荷存在于扭曲上同调理论中的提议。
英文摘要：
We uncover higher algebraic structures on Noether currents and BPS charges. It is known that equivalence classes of conserved currents form a Lie algebra. We show that at least for target space symmetries of higher parameterized WZW-type sigma-models this naturally lifts to a Lie (p+1)-algebra structure on the Noether currents themselves. Applied to the Green-Schwarz-type action functionals for super p-brane sigma-models this yields super Lie (p+1)-algebra refinements of the traditional BPS brane charge extensions of supersymmetry algebras. We discuss this in the generality of higher differential geometry, where it applies also to branes with (higher) gauge fields on their worldvolume. Applied to the M5-brane sigma-model we recover and properly globalize the M-theory super Lie algebra extension of 11-dimensional superisometries by 2-brane and 5-brane charges. Passing beyond the infinitesimal Lie theory we find cohomological corrections to these charges in higher analogy to the familiar corrections for D-brane charges as they are lifted from ordinary cohomology to twisted K-theory. This supports the proposal that M-brane charges live in a twisted cohomology theory.
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