论文标题
相互作用混乱和无序系统的超对称方法：SYK模型
Supersymmetry method for interacting chaotic and disordered systems: the SYK model
论文作者
论文摘要
非线性超质量$σ$ - 模型广泛用于了解安德森本地化的物理和非互操作无序电子系统中的水平统计数据。与普遍认为，超对称方法仅适用于非相互作用粒子系统，我们在相互作用模型中采用这种方法来平均。特别是，我们应用超对称性来研究Sachdev-Ye-Kitaev（Syk）模型，在该模型中，到目前为止，仅在复制方法中进行了平均疾病。我们使用SYK型号的稍微修改的，时空不变的版本，并实时执行计算。为了证明超对称方法的工作原理，我们得出了鞍点方程。在半经典限制中，我们表明结果与使用复制技术发现的结果一致。我们还开发了SYK模型的正式精确超殖民化表示。在后者中，原始费米子及其超级玻色子的超对称理论被重构为无约束的集体激发的模型。我们认为，模型的超对称描述为用于凝结物质，重力和高能量物理的SYK样模型中的精确计算铺平了道路。
The nonlinear supermatrix $σ$-model is widely used to understand the physics of Anderson localization and the level statistics in noninteracting disordered electron systems. In contrast to the general belief that the supersymmetry method applies only to systems of noninteracting particles, we adopt this approach to the disorder averaging in the interacting models. In particular, we apply supersymmetry to study the Sachdev-Ye-Kitaev (SYK) model, where the disorder averaging has so far been performed only within the replica approach. We use a slightly modified, time-reversal invariant version of the SYK model and perform calculations in real-time. As a demonstration of how the supersymmetry method works, we derive saddle point equations. In the semiclassical limit, we show that the results are in agreement with those found using the replica technique. We also develop the formally exact superbosonized representation of the SYK model. In the latter, the supersymmetric theory of original fermions and their superpartner bosons is reformulated as a model of unconstrained collective excitations. We argue that the supersymmetry description of the model paves the way for precise calculations in SYK-like models used in condensed matter, gravity, and high energy physics.
