论文标题
JT超级和布雷津式透明tau功能
JT supergravity and Brezin-Gross-Witten tau-function
论文作者
论文摘要
我们研究Jackiw-Teitelboim（JT）超级重力的热相关函数。我们将重点放在无需时间反向对称性的可定向表面上的JT超级实现的情况下。正如斯坦福（Stanford）和维滕（Witten）最近所示，路径积分量相当于超级黎曼表面的模量空间的体积的计算，其特征在于KDV层次结构的Brezin-gross-witten（BGW）TAU功能。我们发现，JT超级重力的矩阵模型是BGW模型的一种特殊情况，其耦合数的特定方式与Bosonic JT Gravity与Kontsevich-Winter（KW）模型之间的关系类似，以无限的耦合打开。我们计算了JT超级重力的单点功能的属扩展，并研究其低温行为。特别是，我们在贝塞尔情况下提出了单点函数的非扰动完成，其中BGW模型中的所有耦合都设置为零。当Ramond-Ramond通量很大时，我们还会研究自由能和相关器。我们发现，通过定义合适的基础，更高的属自由能的编写与KW模型的形式完全相同，直到统一组的体积的常数术语。这意味着KW模型的构型关系与KDV层次结构的tau功能是普遍的。
We study thermal correlation functions of Jackiw-Teitelboim (JT) supergravity. We focus on the case of JT supergravity on orientable surfaces without time-reversal symmetry. As shown by Stanford and Witten recently, the path integral amounts to the computation of the volume of the moduli space of super Riemann surfaces, which is characterized by the Brezin-Gross-Witten (BGW) tau-function of the KdV hierarchy. We find that the matrix model of JT supergravity is a special case of the BGW model with infinite number of couplings turned on in a specific way, by analogy with the relation between bosonic JT gravity and the Kontsevich-Witten (KW) model. We compute the genus expansion of the one-point function of JT supergravity and study its low-temperature behavior. In particular, we propose a non-perturbative completion of the one-point function in the Bessel case where all couplings in the BGW model are set to zero. We also investigate the free energy and correlators when the Ramond-Ramond flux is large. We find that by defining a suitable basis higher genus free energies are written exactly in the same form as those of the KW model, up to the constant terms coming from the volume of the unitary group. This implies that the constitutive relation of the KW model is universal to the tau-function of the KdV hierarchy.
