论文标题
超对符SYK模型的双缩放极限
The double scaled limit of Super--Symmetric SYK models
论文作者
论文摘要
我们通过使用将分布的矩与方向的和弦图上的总和相关联的组合工具，计算$ \ Mathcal {n} = 2 $ super-Memmetrics Syk模型的确切密度和2点功能，并计算出$ n $ n $双尺度限制中的超级对称SYK模型。特别是我们展示了Susy如何在和弦的希尔伯特（Hilbert）空间（高度退化）上实现。我们以有限的$ n $进行分析计算每个电荷扇区中模型的基态数量，并将其与双尺度限制的结果进行比较。我们的结果减少到低能短相互作用长度限制下的超级切斯瓦兹动作。他们暗示，由于大量的基态，两点函数的保形ANSATZ是不一致的，我们展示了如何添加此贡献。我们还讨论了模型与$ SL_Q（2 | 1）$的关系。为了完整，我们介绍了$ \ Mathcal {n} = 1 $ $ n $双尺度限制中的超级对称SYK模型。
We compute the exact density of states and 2-point function of the $\mathcal{N} =2$ super-symmetric SYK model in the large $N$ double-scaled limit, by using combinatorial tools that relate the moments of the distribution to sums over oriented chord diagrams. In particular we show how SUSY is realized on the (highly degenerate) Hilbert space of chords. We further calculate analytically the number of ground states of the model in each charge sector at finite $N$, and compare it to the results from the double-scaled limit. Our results reduce to the super-Schwarzian action in the low energy short interaction length limit. They imply that the conformal ansatz of the 2-point function is inconsistent due to the large number of ground states, and we show how to add this contribution. We also discuss the relation of the model to $SL_q(2|1)$. For completeness we present an overview of the $\mathcal{N}=1$ super-symmetric SYK model in the large $N$ double-scaled limit.
