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arXiv 1609.01628hep-th
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IIA型超弦矩阵模型中非超对称算子在任意亏格上的单点函数

One-point functions of non-SUSY operators at arbitrary genus in a matrix model for type IIA superstrings

Tsunehide Kuroki, Fumihiko Sugino

摘要:

在前一篇文章中,作者从对称性和谱的观点指出了Ramond-Ramond背景下超对称双阱矩阵模型与二维IIA型超弦理论的对应性。矩阵模型中的平面关联函数和超弦理论中的三能级振幅之间的一致性证实了这一点。为了进一步研究这种对应关系,本文在矩阵模型的双标度极限下,计算了亏格展开各阶的关联函数。受超对称性保护的算子的单点函数终止于某个有限阶,而不受保护的算子的单点函数产生非Borel可和级数。后者的行为是弦微扰级数的特征,提供了矩阵模型描述弦论的进一步证据。此外,还计算了平面单点函数的瞬子修正,并发现了非超对称算子的普遍对数标度行为。

英文摘要:

In the previous paper, the authors pointed out correspondence between a supersymmetric double-well matrix model and two-dimensional type IIA superstring theory on a Ramond-Ramond background from the viewpoint of symmetry and spectrum. This was confirmed by agreement between planar correlation functions in the matrix model and tree-level amplitudes in the superstring theory. In order to investigate the correspondence further, in this paper we compute correlation functions to all order of genus expansion in the double scaling limit of the matrix model. One-point functions of operators protected by supersymmetry terminate at some finite order, whereas those of unprotected operators yield non-Borel summable series. The behavior of the latter is characteristic in string perturbation series, providing further evidence that the matrix model describes a string theory. Moreover, instanton corrections to the planar one-point functions are also computed, and universal logarithmic scaling behavior is found for non-supersymmetric operators.

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