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

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.

v2: Typo in Eq.7 is corrected

References in corpus (8)

• A Large Mass Hierarchy from a Small Extra Dimension
• Quantum Brachistochrone
• Collisions of Cosmic F- and D-strings
• Planetoid String Solutions in 3 + 1 Axisymmetric Spacetimes
• Black Holes and Causal Structure in Anti-de Sitter Isometric Spacetimes
• Rigidly Rotating Strings in Stationary Spacetimes
• New Classes of Exact Multi-String Solutions in Curved Spacetimes
• Classification of Cohomogeneity One Strings

Cited by in corpus (11)

• Universality in Chaos of Particle Motion near Black Hole Horizon
• The fate of chaotic strings in a confining geometry
• Stationary Rotating Strings as Relativistic Particle Mechanics
• Exactly solvable strings in Minkowski spacetime
• Dynamics of Toroidal Spiral Strings around Five-dimensional Black Holes
• Toroidal Spiral Nambu-Goto Strings around Higher-Dimensional Black Holes
• Rigidly Rotating String Sticking in a Kerr Black Hole
• Membranes with a symmetry of cohomogeneity one
• Perturbations of Spacetime around a Stationary Rotating Cosmic String
• Stationary Closed Strings in Five-dimensional Flat Spacetime
• Note on orbit space of G membranes