arXiv 1509.050332015-09-16hep-th

AdS $_3$中弦上的碰撞波

Colliding waves on a string in AdS$_3$

David Vegh

备注：: 9 pages, 16 figures

摘要：

本文研究整体AdS $_3$中弦的经典运动。最初静止的弦在边界圆上的两个对跖点之间伸展。两个端点都受到扰动，以稳定的速率产生尖点。尖点向它们碰撞的内部传播。弦的行为取决于力的强度。可以区分出三种不同性质的相：透明、灰色和黑色。透明区域类似于驻波。在黑色阶段，世界表上有一个地平线，尖点永远不会到达另一个端点。弦不断折叠，其长度随时间线性增长。在灰色阶段，字符串仍然线性增长。然而，尖点确实会交叉到另一边。透明区域和灰色区域由过渡点分开，在过渡点处，数值上观察到尖点的对数累积。一个简单的模型再现了弦在这三个阶段的定性行为。

英文摘要：

This paper is concerned with the classical motion of a string in global AdS$_3$. The initially static string stretches between two antipodal points on the boundary circle. Both endpoints are perturbed which creates cusps at a steady rate. The cusps propagate towards the interior where they collide. The behavior of the string depends on the strength of forcing. Three qualitatively different phases can be distinguished: transparent, gray, and black. The transparent region is analogous to a standing wave. In the black phase, there is a horizon on the worldsheet and cusps never reach the other endpoint. The string keeps folding and its length grows linearly over time. In the gray phase, the string still grows linearly. However, cusps do cross to the other side. The transparent and gray regions are separated by a transition point where a logarithmic accumulation of cusps is numerically observed. A simple model reproduces the qualitative behavior of the string in the three phases.

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