Single spike solutions for strings on S2 and S3

Abstract

We study solutions for rigidly rotating strings on a two sphere. Among them we find two limiting cases that have a particular interest, one is the already known giant magnon and the other we call the single spike solution. The limiting behavior of this last solution is a string infinitely wrapped around the equator. It differs from that solution by the existence of a single spike of height theta that points toward the north pole. We study its properties and compute its energy E and angular momentum J as a function of theta. We further generalize the solution by adding one angular momentum to obtain a solution on S3. We find a spin chain interpretations of these results in terms of free fermions and the Hubbard model but the exact relation with the same models derived from the field theory is not clear.

LaTeX, 20 pages, 3 figures. v2: Refs added

References in corpus (5)

• Gauge invariant finite size spectrum of the giant magnon
• Spiky Strings, Giant Magnons and beta-deformations
• On the anatomy of multi-spin magnon and single spike string solutions
• Neumann and Neumann-Rosochatius integrable systems from membranes on AdS_4xS^7
• On the multi-spin magnon and spike solutions from membranes

Cited by in corpus (11)

• Strong-coupling expansion of cusp anomaly and gluon amplitudes from quantum open strings in AdS_5 x S^5
• Spiky Strings, Giant Magnons and beta-deformations
• On the anatomy of multi-spin magnon and single spike string solutions
• Neumann and Neumann-Rosochatius integrable systems from membranes on AdS_4xS^7
• Aspects of Integrability in AdS/CFT Duality
• On the multi-spin magnon and spike solutions from membranes
• Fundamental String and D1-brane in I-brane Background
• Sum rules for higher twist sl(2)operators in N=4 SYM
• Spin chain from membrane and the Neumann-Rosochatius integrable system
• N-body Dynamics of Giant Magnons in RxS2
• Conformal SO(2,4) Transformations for the Helical AdS String Solution