Pair-production of cusps on a string in AdS$_3$

TL;DR

This paper investigates the classical dynamics of strings in AdS$_3$, revealing that boundaries between sinh-Gordon and cosh-Gordon regions can produce cusp pairs, leading to a transition from a segmented string to a cusp gas.

Contribution

It demonstrates classical pair-production of cusps at soliton boundaries in AdS$_3$ string solutions, using exact discretization and segmented strings, revealing a new dynamical process.

Findings

Pair-production of cusps occurs at soliton boundaries moving at light speed.

Energy cascades during cusp pair-creation, leading to evaporation of sinh-Gordon regions.

Final state is a cusp gas in a cosh-Gordon environment.

Abstract

The classical motion of a Nambu-Goto string in AdS$_3$ spacetime is governed by the generalized sinh-Gordon equation. It can locally be reduced to the sinh-Gordon (shG), cosh-Gordon (chG), or Liouville equation, depending on the value of the scalar curvature of the induced metric. In this paper, I examine solutions that contain both shG-type and chG-type regions. The boundary between these regions moves with the speed of light. I show that near such boundaries (generalized) solitons can be classically pair-produced. The solitons move subluminally (superluminally) in the shG (chG) region on the worldsheet, and they correspond to cusps on the string. A direct energy cascade is observed at the moment of pair-creation. For the calculations, I use an exact discretization of the equation of motion. The solutions are segmented strings. In this discrete system, pair-production leads to a complete evaporation of the shG region. The final state is a gas of cusps in a chG environment. A Mathematica notebook that has been used to generate the relevant figures is attached.