全息对偶原理在强耦合场论系统热化过程中的应用

Thermalization process, especially for strongly coupled systems, is an important but unsolved problem in modern theoretical physics. AdS/CFT, or the generic holographic principle, provides us powerful tools to deal with strongly coupled field systems, applying which we can understand the thermalization process of strongly coupled field system through studying the black hole formation process in dual gravitational system. In current project, we plan to study the thermalization process of strongly coupled field systems through holographic principle. The project contains two main parts:.1. Thermalization process of field systems living in curved background. At this time, the dual spacetime is still an asymptotical AdS spacetime, but with a curved boundary instead of a flat one. We will investigate the influence of curved boundary on the thermalization process in various collapsing models..2. Thermalization process described by exact analytical dynamical black hole solutions. At this time, the black hole formation process is described by analytical dynamical metric. By studying the corresponding thermalization process, we hope to find some analytical and universal properties about the strongly coupled field systems..In both two parts, we will investigate the evolution of various observable, especially the entanglement entropy, in the thermalization process.

热化过程，特别是强耦合场论系统的热化过程，一直是理论物理的前沿热门课题以及难题。AdS/CFT，或者更一般的全息对偶原理，则为我们提供了研究强耦合场论系统的强有力的工具。根据此原理， 我们可以通过研究弱引力系统中的黑洞形成过程来给出边界强耦合场论系统的热化过程。在本项目中，我们计划利用全息对偶原理研究强耦合场论系统的热化过程。内容主要分为两个方面：.1. 弯曲时空背景中场论系统的热化过程。此时对偶引力时空仍然是渐近AdS时空，但是具有弯曲而不是平坦的边界。我们将考察在各种不同的黑洞形成模型下，边界弯曲对热化过程的影响。.2. 精确解析的动态黑洞解所描述的热化过程。此时描述黑洞形成过程的度规是精确解析的。通过研究这些解对应的热化过程，我们期望从中得到强耦合场论系统的一些解析的、普适的性质。.在这两个研究方面，我们将考察各类观测量，尤其是纠缠熵在热化过程中的演化行为。

本项目尝试利用全息对偶原理研究强耦合场论系统热化过程这一理论难题。.主要研究内容有两方面：（1）全息QCD模型中禁闭/退禁闭相变过程中系统纠缠熵和复杂度的变化；（2）强耦合场论系统热化过程中系统纠缠熵和复杂度的变化。.主要研究结果：（1）在强耦合系统相变过程中，纠缠熵和复杂度的行为能很好的反映相变的类型和相变点，因此可以当做描述强耦合系统相变过程的序参量；（2）强耦合场论系统热化过程中子域复杂度的一般演化行为，并且这些行为与系统所处的时空背景关系不大。这些结果对于我们进一步理解强耦合系统的性质具有十分重要的意义和启发。