Title: AdS/CFT correspondence, quasinormal modes, and thermal correlators in N=4 SYM Show Chinese title

Title: AdS/CFT 对应关系，准正模，以及 N=4 SYM 中的热关联函数

Abstract: We use the Lorentzian AdS/CFT prescription to find the poles of the retarded thermal Green's functions of ${\cal N=4}$ SU(N) SYM theory in the limit of large N and large 't Hooft coupling. In the process, we propose a natural definition for quasinormal modes in an asymptotically AdS spacetime, with boundary conditions dictated by the AdS/CFT correspondence. The corresponding frequencies determine the dispersion laws for the quasiparticle excitations in the dual finite-temperature gauge theory. Correlation functions of operators dual to massive scalar, vector and gravitational perturbations in a five-dimensional AdS-Schwarzschild background are considered. We find asymptotic formulas for quasinormal frequencies in the massive scalar and tensor cases, and an exact expression for vector perturbations. In the long-distance, low-frequency limit we recover results of the hydrodynamic approximation to thermal Yang-Mills theory. Show Chinese abstract

Abstract: 我们利用Lorentzian AdS/CFT方法，研究了在大N和大't Hooft耦合极限下，${\cal N=4}$ SU(N)规范理论的热耗散Green函数的极点。在此过程中，我们提出了渐近AdS时空准正规模态的一个自然定义，并由AdS/CFT对偶给出边界条件。对应的频率决定了对偶有限温度规范理论中准粒子激发的色散关系。考虑了五维AdS-Schwarzschild背景下，与质量标量、矢量及引力扰动相对应算符的相关函数。我们得到了质量标量和张量情形下的准正规模态频率的渐近公式，以及矢量扰动的精确表达式。在长距离、低频极限下，我们得到了热Yang-Mills理论流体力学近似的结论。