Perturbations of spiky strings in AdS3

TL;DR

This paper studies small perturbations of spiky strings in AdS3, showing they are stable against fluctuations by solving a special case of the DTV equation numerically.

Contribution

It demonstrates the stability of AdS3 spiky strings under small perturbations using the DTV equation and numerical solutions of eigenvalues and eigenfunctions.

Findings

Spiky strings in AdS3 are stable against small fluctuations.

The perturbation equation reduces to a DTV equation.

Numerical solutions confirm finite perturbations exist.

Abstract

Perturbations of a class of semiclassical spiky strings in three dimensional Anti-de Sitter (AdS) spacetime, are investigated using the well-known Jacobi equations for small, normal deformations of an embedded timelike surface. We show that the equation for the perturbation scalar which governs the behaviour of such small deformations, is a special case of the well-known Darboux-Treibich-Verdier (DTV) equation. The eigenvalues and eigensolutions of the DTV equation for our case are obtained by solving certain continued fractions numerically. These solutions are thereafter utilised to further demonstrate that there do exist finite perturbations of the AdS spiky strings. Our results therefore establish that the spiky string configurations in AdS3 are indeed stable against small fluctuations. Comments on future possibilities of work are included in conclusion.