论文标题
在任意属的两点功能及其在2D类型IIA SuperSrings的矩阵模型中的复发结构
Two-point functions at arbitrary genus and its resurgence structure in a matrix model for 2D type IIA superstrings
论文作者
论文摘要
在先前的论文中，指出的是超对称的双孔基质模型对应于在相关函数级别的Ramond-ramond背景上的二维IIA超弦理论。通过其平面相关函数之间的一致性证实了这一点。矩阵模型中的超对称性对应于目标空间超对称性，并通过非扰动效应自发地破坏了目标空间。此外，在矩阵模型中，我们将单个跟踪操作员的单点函数计算为在其双缩放限制中的所有属扩展顺序。我们发现，这种扩展是严格的，而不是可以总结的，因此在应用Borel重新召集技术时产生了歧义。我们确认在这里的复兴有效，即在零-instanton部门的扰动序列中的这种歧义是由Instanton计算获得的一单位式部门中的另一个歧义完全取消的。在本文中，我们扩展了单个微量运算符的两点函数的分析和研究复兴结构。通过在随机矩阵理论中使用结果，我们在任意属上得出了两点函数，并看到零in-Instanton部门中的扰动序列再次具有歧义。我们发现，即使在较高的属处，两点函数也不可避免地具有对数奇异性。在此推导中，我们获得了由一分点函数在领先顺序上表达的两点函数的新结果，以随机矩阵理论的软边尺度限制。我们还通过使用通风的内核来计算一阵容扇区的歧义，并确认这两个部门的歧义在双缩放限制中以领先顺序相互抵消。因此，我们阐明了超对称双孔矩阵模型中两点函数的重新表现结构。
In the previous papers, it is pointed out that a supersymmetric double-well matrix model corresponds to a two-dimensional type IIA superstring theory on a Ramond-Ramond background at the level of correlation functions. This was confirmed by agreement between their planar correlation functions. The supersymmetry in the matrix model corresponds to the target space supersymmetry and it is shown to be spontaneously broken by nonperturbative effect. Furthermore, in the matrix model we computed one-point functions of single-trace operators to all order of genus expansion in its double scaling limit. We found that this expansion is stringy and not Borel summable and hence there arises an ambiguity in applying the Borel resummation technique. We confirmed that resurgence works here, namely this ambiguity in perturbative series in a zero-instanton sector is exactly canceled by another ambiguity in a one-instanton sector obtained by instanton calculation. In this paper we extend this analysis and study resurgence structure of the two-point functions of the single trace operators. By using results in the random matrix theory, we derive two-point functions at arbitrary genus and see that the perturbative series in the zero-instanton sector again has an ambiguity. We find that the two-point functions inevitably have logarithmic singularity even at higher genus. In this derivation we obtain a new result of the two-point function expressed by the one-point function at the leading order in the soft-edge scaling limit of the random matrix theory. We also compute an ambiguity in the one-instanton sector by using the Airy kernel, and confirm that ambiguities in both sectors cancel each other at the leading order in the double scaling limit. We thus clarify resurgence structure of the two-point functions in the supersymmetric double-well matrix model.
