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arXiv 0904.2303hep-th
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弦论中的大D-瞬子效应

Large D-instanton effects in string theory

Boris Pioline, Stefan Vandoren

摘要:

通过沿时间方向的约化,四维的黑洞产生三维的瞬子。这些瞬子中的每一个都以$\exp(-|Q|/g_s)$的数量级对三维有效作用量中的某些受保护耦合做出贡献,但是不同瞬子的数量预计与黑洞微态的数量相等(或相当),即具有$\exp(Q^2)$的数量级。同样的现象也发生在四维中某些受保护的耦合中,例如在卡-丘三重空间上紧化的II型弦论中的超多重态度规。因此,在任何一种情况下,D-瞬子级数都是渐近的,很像任何量子场论中的微扰展开。通过使用适应D-瞬子序列高斯增长的Borel型求和方法,我们发现总D-瞬子和具有$\exp(-1/g_s^2)$阶的固有模糊性。我们进一步建议,这种模糊性可以通过包括卡鲁扎-克莱因瞬子或NS 5-膜瞬子来消除。

英文摘要:

By reduction along the time direction, black holes in 4 dimensions yield instantons in 3 dimensions. Each of these instantons contributes individually at order $\exp(-|Q|/g_s)$ to certain protected couplings in the three-dimensional effective action, but the number of distinct instantons is expected to be equal (or comparable) to the number of black hole micro-states, i.e. of order $\exp(Q^2)$. The same phenomenon also occurs for certain protected couplings in four dimensions, such as the hypermultiplet metric in type II string theories compactified on a Calabi-Yau threefold. In either case, the D-instanton series is therefore asymptotic, much like the perturbative expansion in any quantum field theory. By using a Borel-type resummation method, adapted to the Gaussian growth of the D-instanton series, we find that the total D-instanton sum has an inherent ambiguity of order $\exp(-1/g_s^2)$. We further suggest that this ambiguity can be lifted by including Kaluza-Klein monopole or NS5-brane instantons.

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