The broken string in anti-de Sitter space

TL;DR

This paper introduces an efficient method for solving classical string equations in (2+1)-dimensional anti-de Sitter space, enabling accurate approximations of smooth string motions and analyzing cusp dynamics.

Contribution

It presents a novel approach to approximate string solutions in AdS space, including cusp behavior and collision dynamics, suitable for numerical simulations.

Findings

Exact piecewise linear string solutions in AdS

Cusps move at light speed and collide with a specific formula

Method effectively models string behavior ending on boundary quarks

Abstract

This paper describes an efficient method for solving the classical string equations of motion in (2+1)-dimensional anti-de Sitter spacetime. Exact string solutions are identified that are the analogs of piecewise linear strings in flat space. They can be used to approximate any smooth string motion to arbitrary accuracy. Cusps on the string move with the speed of light and their collisions are described by a Picard-Lefschetz-type formula. Explicit examples are shown with the string ending on two boundary quarks. The technique is ideally suited for numerical simulations. A Mathematica notebook that has been used to generate the relevant figures is also included.