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arXiv 1710.00545hep-th
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AdS(3)中的椭圆弦解和AdS(4)中的椭圆极小曲面

Elliptic String Solutions in AdS(3) and Elliptic Minimal Surfaces in AdS(4)

Georgios Pastras

摘要:

定义在对称目标空间上的非线性西格玛模型在现代物理学中有着广泛的应用,包括描述弦在对称空间中的传播,如AdS或dS,或双曲空间中的极小曲面。虽然由于这些模型的非线性性质,很难获得它们的解,但众所周知,它们可约化为正弦或sinh-Gordon方程族的可积系统。在这项研究中,我们开发了一种方法来反转Pohlmeyer约化的椭圆形解决方案的减少系统,实现NLSM解决方案和本征态的n = 1拉梅问题之间的关系。应用这种方法产生了AdS(3)中的一类经典弦解,其中包括尖弦解以及角速度和半径奇异演化的环弦解,这些解在全息对偶的框架下是有趣的.此外,这种方法的应用产生了一个广泛的家庭的静态最小曲面在AdS(4),其中包括螺旋面和catenoid,这是有趣的Ryu-Takayanagi猜想的框架和理解的出现,引力作为一个熵力与量子纠缠统计。开发的形式主义允许的最小表面和它们之间的几何相变,这是相关的限制-解除限制相变的面积的研究。

英文摘要:

Non-linear sigma models defined on symmetric target spaces have a wide set of applications in modern physics, including the description of string propagation in symmetric spaces, such as AdS or dS, or minimal surfaces in hyperbolic spaces. Although it is difficult to acquire solutions of these models, due to their non-linear nature, it is well known that they are reducible to integrable systems of the family of the sine- or sinh-Gordon equation. In this study, we develop a method to invert Pohlmeyer reduction for elliptic solutions of the reduced system, implementing a relation between NLSM solutions and the eigenstates of the n = 1 Lame problem. This method is applied to produce a family of classical string solutions in AdS(3), which includes the spiky strings, as well as hoop string solutions with singular evolution of their angular velocity and radius, which are interesting in the framework of holographic dualities. Furthermore, application of this method produces a wide family of static minimal surfaces in AdS(4), which includes helicoids and catenoids, and which are interesting in the framework of the Ryu-Takayanagi conjecture and the understanding of the emergence of gravity as an entropic force related to quantum entanglement statistics. The developed formalism allows the study of the area of the minimal surfaces and geometric phase transitions between them, which are relevant to confinement-deconfinement phase transitions.

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