论文标题
关于副本法和sachdev-ye-kitaev模型的评论
Remarks on Replica Method and Sachdev-Ye-Kitaev Model
论文作者
论文摘要
通过追踪到EA/SK模型，我们将删除SYK模型的构造逻辑。在施工期间，我们回想起复制方法的技术本质。然后，我们指出了通过从2个索引SY模型到其4个索引版本的概括，从2个索引模型到其4个索引版本的概述，并从Majoraana fermions来简化后者。壮观地，这样的简化保留了系统的自洽条件。摆脱冗余，模型本身及其有效的动作具有相同的$ O（N_S）$结构对称性，而它通过新兴的保形对称性实现了$ aDS_2/cft_1 $全息图。我们还阐明了对矩阵模型的模型trans变，并认为疾病平均的SYK模型自然保留了全息性质。基于trans变和与向量模型的对应关系，SYK模型正式是这两个模型的混合体。还分别讨论了其量子和半古老特性。
Through tracing back to EA/SK models, we disentangle the construction logic of SYK model. During the construction, we recall the technical essence of replica method. Then we point out the redundance of the flavor group and the slave indices as well as the color group via the generalization from 2-index SY model to its 4-index version and the simplification of the latter in terms of Majorana fermions. Spectacularly, such a simplification reserves the system's self-consistency condition. Getting rid of the redundance, the model itself and its effective action have the same $O(N_s)$ structural symmetry, while it realizes $AdS_2/CFT_1$ holography by the emergent conformal symmetry. We also clarify the model transmutation to matrix model and argue that the disorder-averaged SYK model naturally preserves a holographic nature. Based on the transmutation and the correspondence with vector model, SYK model is formally a hybrid of these two models. Its quantum and semiclassical properties are also discussed respectively.
