Strings in five-dimensional anti-de Sitter space with a symmetry

TL;DR

This paper classifies string solutions in five-dimensional anti-de Sitter space using symmetry and cohomogeneity concepts, introduces a new solution with unique properties, and analyzes its geometry as a timelike helicoid-like surface.

Contribution

It develops a classification method for extended objects in symmetric spacetimes and finds a novel string solution specific to odd-dimensional anti-de Sitter spaces.

Findings

Classified all string solutions in 5D anti-de Sitter space.

Discovered a new timelike helicoid-like string solution.

Analyzed the geometry of the new solution.

Abstract

The equation of motion of an extended object in spacetime reduces to an ordinary differential equation in the presence of symmetry. By properly defining of the symmetry with notion of cohomogeneity, we discuss the method for classifying all these extended objects. We carry out the classification for the strings in the five-dimensional anti-de Sitter space by the effective use of the local isomorphism between $\SO(4,2)$ and $\SU(2,2)$. We present a general method for solving the trajectory of the Nambu-Goto string and apply to a case obtained by the classification, thereby find a new solution which has properties unique to odd-dimensional anti-de Sitter spaces. The geometry of the solution is analized and found to be a timelike helicoid-like surface.