本项目研究规范/引力对偶在强耦合体系中的应用。着重在作为规范场/引力场对偶微观实现例子的Sachdev-Ye-Kitaev(SYK)模型及其引力对偶。为了理解奇异金属高温超导体及强耦合体系的物理性质，拟推广SYK模型并计算热电系数、洛伦茨数、霍尔角、能斯特信号、磁阻以及蝴蝶速度，发展超导配对理论、Riordan-Touchard 高维形式，期望较解析地实现磁场下非费米液体行为，理解多体局域相变，得到与实验数据符合的结果。另一方面，SYK模型也提供了一个途径来探索量子引力效应。故拟研究SYK模型的引力对偶，寻找与bulk弦论alpha’展开、经典引力的量子修正、弦/引力对偶、全息布朗运动的联系。作为研究结果的补充支持，对加入轴子场的全息费米子系统展开相关研究。此外，拟推广基于规范/引力对偶的Witten-Sakai-Sugimoto(WSS)模型，为低能QCD非微扰强耦合色紧闭问题提供线索。

This project deals with the application of gauge/gravity duality in strong coupling system, especially the sachdev-ye-kitaev (SYK) model and its gravity duality. SYK model is an example of gauge field/gravitational field microscopically correspondence. In order to understand the physical properties of strange metal, based on the extension of SYK model, we investigate the thermoelectric coefficient, lorentz number, hall angle, nernst signal, the magnetic resistance, butterfly velocity, the pairing theory of superconductivity and high-dimensional Riordan-Touchard formula. Via the SYK model, we intend to analytically realize the behavior of non-fermi liquid under magnetic field, understand many-body local phase transformation, and compare with the experimental data. On the other hand, the SYK model also provides a method to explore quantum gravity effects. Therefore, it is proposed to study the gravitational duality of the SYK model, such as the correspondence with the alpha` expansion in string theory, the quantum correction of classical gravity, string/gravity duality and holographic brownian motion. In addition, as a supplement for the research results, the holographic fermion system with the axion field is investigated. Besides, we propose to generalize the witten-sakai-sugimoto (WSS) model, which is based on the gauge/gravity duality. It provides some useful clues for the non-perturbative strong-coupling phenomenon and color confinement in the low energy region.