论文标题
复杂的sachdev-ye-kitaev模型在双缩放限制中
Complex Sachdev-Ye-Kitaev model in the double scaling limit
论文作者
论文摘要
我们在所有能量尺度的双尺度限制下，在复杂SYK模型的确切能量谱，2分和4分函数上求解。该型号具有$ u（1）$全球对称性。分析显示了如何将化学电位纳入和弦图图片中，我们在给定的固定电荷扇区也为各种可观察物提供了结果。除了与光谱不对称匹配外，我们还考虑了2分函数的类似不对称度量，以遵守对操作员维度的非平凡依赖性。我们还为类似Syk的模型提供了和弦图结构，该模型在任何障碍实现时都具有$ U（m）$全球对称性。然后，我们展示如何与正式无限的共形维度精确计算插入非常重的操作员的效果。后者将重力时空分为通过界面连接的几个部分，其属性在所有尺度上都是可计算的。特别是，足够轻的状态仍然可以在空间之间进行。在和弦图图中，此行为具有简单的描述。
We solve for the exact energy spectrum, 2-point and 4-point functions of the complex SYK model, in the double scaling limit at all energy scales. This model has a $U(1)$ global symmetry. The analysis shows how to incorporate a chemical potential in the chord diagram picture, and we present results for the various observables also at a given fixed charge sector. In addition to matching to the spectral asymmetry, we consider an analogous asymmetry measure of the 2-point function obeying a non-trivial dependence on the operator's dimension. We also provide the chord diagram structure for an SYK-like model that has a $U(M)$ global symmetry at any disorder realization. We then show how to exactly compute the effect of inserting very heavy operators, with formally infinite conformal dimension. The latter separate the gravitational spacetime into several parts connected by an interface, whose properties are exactly computable at all scales. In particular, light enough states can still go between the spaces. This behavior has a simple description in the chord diagram picture.
