On Elliptic String Solutions in AdS(3) and dS(3)

Abstract

Classical string actions in AdS(3) and dS(3) can be connected to the sinh-Gordon and cosh-Gordon equations through Pohlmeyer reduction. We show that the problem of constructing a classical string solution with a given static or translationally invariant Pohlmeyer counterpart is equivalent to solving four pairs of effective Schrodinger problems. Each pair consists of a flat potential and an n = 1 Lame potential whose eigenvalues are connected, and, additionally, the four solutions satisfy a set of constraints. An approach for solving this system is developed by employing an interesting connection between the specific class of classical string solutions and the band structure of the Lame potential. This method is used for the construction of several families of classical string solutions, one of which turns out to be the spiky strings in AdS(3). New solutions include circular rotating strings in AdS(3) with singular time evolution of their radius and angular velocity as well as classical string solutions in dS(3).

60 pages, 13 figures, v2: version to appear in JHEP after minor corrections

References in corpus (12)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Gluon scattering amplitudes at strong coupling
• Pohlmeyer reduction of AdS_5 x S^5 superstring sigma model
• Dyonic Giant Magnons
• Generating AdS String Solutions
• Pohlmeyer reduction revisited
• On reduced models for superstrings on AdS_n x S^n
• Solitons and AdS String Solutions
• Magnons, their Solitonic Avatars and the Pohlmeyer Reduction
• Sine-Gordon-like action for the Superstring in AdS(5) x S(5)
• Moduli Dynamics of AdS_3 Strings
• Dual Spikes; New Spiky String Solutions

Cited by in corpus (11)

• Degenerate multi-solitons in the sine-Gordon equation
• Static Elliptic Minimal Surfaces in AdS(4)
• Minimal n-Noids in hyperbolic and anti-de Sitter 3-space
• Dressed Elliptic String Solutions on RxS^2
• Salient Features of Dressed Elliptic String Solutions on $\mathbb{R}\times$S${}^2$
• Stability Analysis of Classical String Solutions and the Dressing Method
• Elliptic String Solutions on RxS^2 and Their Pohlmeyer Reduction
• The Dressing Method as Non Linear Superposition in Sigma Models
• Mass and spin for classical strings in $d{S}_3$
• Revisiting the O(3) Non-linear Sigma Model and Its Pohlmeyer Reduction
• Novel aspects of integrability for NLSMs in symmetric spaces