本文通过两种方法推导了大$ p $ SYK模型的非线性有效作用，展示了该模型在微观动力学控制方面的独特性。
摘要：
在低温下，SYK模型的物理行为主要由一个由Schwarzian作用支配的软模所主导。在arXiv:1604.07818中，已经从四点函数的软模贡献中推导出了线性化作用，并给出了其非线性完成到Schwarzian的物理论证。在本文中，我们给出了在大$ p $极限下完整非线性有效作用的两个推导，其中$ p $是哈密顿量相互作用项中费米子的数量。第一个推导利用了大$ p $ SYK模型的集体场作用是Liouville理论，其具有非共形边界条件，我们通过共形扰动理论进行研究。这一推导可以被视为arXiv:1711.08467中非线性软模作用的重整化群论证的显式版本。第二个推导则利用了软模如何嵌入到集体场的微观配置空间中的假设。我们推广了对于大$ p $ SYK链的结果，并获得了其对应的
英文摘要：
The physics of the SYK model at low temperatures is dominated by a soft mode governed by the Schwarzian action. In arXiv:1604.07818 the linearised action was derived from the soft mode contribution to the four-point function, and physical arguments were presented for its nonlinear completion to the Schwarzian. In this paper, we give two derivations of the full nonlinear effective action in the large $p$ limit, where $p$ is the number of fermions in the interaction terms of the Hamiltonian. The first derivation uses that the collective field action of the large-$p$ SYK model is Liouville theory with a non-conformal boundary condition that we study in conformal perturbation theory. This derivation can be viewed as an explicit version of the renormalisation group argument for the nonlinear soft mode action in arXiv:1711.08467. The second derivation uses an Ansatz for how the soft mode embeds into the microscopic configuration space of the collective fields. We generalise our results for the large-$p$ SYK chain and obtain a "Schwarzian chain" effective action for it. These derivations showcase that the large-$p$ SYK model is a rare system, in which there is sufficient control over the microscopic dynamics, so that an effective description can be derived for it without the need for extra assumptions or matching (in the effective field theory sense).
All-order fluctuating hydrodynamics of the SYK lattice
Mathematical Institute, University of Oxford（牛津大学数学研究所）；Institute for Quantum Information and Matter, California Institute of Technology（加州理工学院量子信息与物质研究所）；Department of Physics and Astronomy, University of Kentucky（肯塔基大学物理与天文学系）
