2+1维共形场论中的色散拟正规模
Dispersing quasinormal modes in 2+1 dimensional conformal field theories
摘要：
利用AdS/CFT对应研究了2+1维非零温度下共形场论（CFTs）的电荷响应。一个中心的作用是由准正规模式（QNM），具体地说，极点和零点的电流放大器。我们推广了我们最近的研究QNM的交流。电荷电导率包括动量依赖性。这揭示了在CFT的各种激励。我们首先利用全息术讨论了N=8 SU（N）超杨-米尔斯理论在共形不动点处的R-电流算符。例如，QNM光谱中的跃迁作为动量的函数，清楚地识别了流体动力学到相对论的交叉。然后，我们将我们的研究扩展到引力描述中的四阶导数项，使我们能够研究更一般的电荷响应以及S-对偶性的作用，S-对偶性在理解引力子中起着核心作用。分散的类德鲁德QNM的存在可以导致新的行为，与上述规范理论中发生的不同。我们还扩展了以前的电导率和规则有限动量和讨论他们的解释在重力图片。最后与向量O（N）模型在大N极限下的共形不动点作了比较。
英文摘要：
We study the charge response of conformal field theories (CFTs) at non-zero temperature in 2+1 dimensions using the AdS/CFT correspondence. A central role is played by the quasinormal modes (QNMs), specifically, the poles and zeros of the current correlators. We generalize our recent study of the QNMs of the a.c. charge conductivity to include momentum dependence. This sheds light on the various excitations in the CFT. We begin by discussing the R-current correlators of the N=8 SU(N) super-Yang-Mills theory at its conformal fixed point using holography. For instance, transitions in the QNM spectrum as a function of momentum clearly identify hydrodynamic-to-relativistic crossovers. We then extend our study to include four-derivative terms in the gravitational description allowing us to study more generic charge response as well as the role of S-duality, which plays a central role in understanding the correlators. The presence of dispersing Drude-like QNMs can lead to new behavior, distinct from what occurs in the aforementioned gauge theory. We also extend previous conductivity sum rules to finite momentum and discuss their interpretation in the gravity picture. A comparison is finally made with the conformal fixed point of the vector O(N) model in the large-N limit.
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