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

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Cited by in corpus (62)

• Strong-coupling expansion of cusp anomaly and gluon amplitudes from quantum open strings in AdS_5 x S^5
• Moduli Dynamics of AdS_3 Strings
• Neumann-Rosochatius integrable system for strings on AdS_4 x CP^3
• Finite Size Giant Magnon
• Spiky Strings, Giant Magnons and beta-deformations
• On the Rotating and Oscillating strings in $(Ad{S}_3\times S^3{)}_{\varkappa }$
• Correlation functions of magnon and spike
• Scattering of single spikes
• On the anatomy of multi-spin magnon and single spike string solutions
• Spiky strings on AdS3 x S3 with NS-NS flux
• Giant magnons and spiky strings on the conifold
• Review of AdS/CFT Integrability, Chapter II.1: Classical AdS5xS5 string solutions
• Giant Magnons in AdS4 x CP3: Embeddings, Charges and a Hamiltonian
• Neumann and Neumann-Rosochatius integrable systems from membranes on AdS_4xS^7
• Correlation function of dyonic strings
• Massless sector of AdS_3 superstrings: a geometric interpretation
• Magnon like solutions for strings in I-brane background
• Aspects of Integrability in AdS/CFT Duality
• Finite size effect on the magnon's correlation functions
• New open string solutions in AdS_5
• On the multi-spin magnon and spike solutions from membranes
• Spiky strings in $\varkappa$-deformed $AdS$
• Spiky Strings on NS5-branes
• Decoding the Spin-Matrix limit of strings on $Ad{S}_5\times S^5$
• Giant Magnons and Spiky Strings on S^3 with B-field
• Sum rules for higher twist sl(2)operators in N=4 SYM
• Fundamental String and D1-brane in I-brane Background
• Spiky Strings in AdS(4) X CP**3 with Neveu-Schwarz Flux
• Strings on the deformed T^{1,1}: giant magnon and single spike solutions
• Spin chain from membrane and the Neumann-Rosochatius integrable system
• Negative anomalous dimensions in N=4 SYM
• Rotating Strings in AdS(4) X CP(3) with B-NS holonomy
• Nonrelativistic giant magnons from Newton Cartan strings
• Large-Spin and Large-Winding Expansions of Giant Magnons and Single Spikes
• N-body Dynamics of Giant Magnons in RxS2
• Semiclassical strings in AdS(3) X S^2
• Conformal SO(2,4) Transformations for the Helical AdS String Solution
• Dressed Elliptic String Solutions on RxS^2
• Duality and Decay of Macroscopic F-Strings
• Salient Features of Dressed Elliptic String Solutions on $\mathbb{R}\times$S${}^2$
• D1 string dynamics in curved backgrounds with fluxes
• Stability Analysis of Classical String Solutions and the Dressing Method
• Spiky strings in de Sitter space
• Correlation functions of the ABJM model
• Elliptic String Solutions on RxS^2 and Their Pohlmeyer Reduction
• Perturbations of spiky strings in AdS3
• Three Spin Spiky Strings in beta-deformed Background
• Giant Spinons
• Neumann-Rosochatius system for (m,n) string in $Ad{S}_3\times S^3$ with mixed flux
• Divergent energy strings in $Ad{S}_5\times S^5$ with three angular momenta
• Semiclassical Strings in Supergravity PFT
• N spike D-strings in AdS Space with mixed flux
• On Rotating and Oscillating Four-Spin Strings in AdS5 X S5
• Some comments about emission channels of non abelian vortices
• $SL(2,Z)$ invariant rotating $(m,n)$ strings in $Ad{S}_3\times S^3$ with mixed flux
• Neumann-Rosochatius system for strings on I-brane
• Finite Size Effect from Classical Strings in deformed AdS${}_3\times$ S${}^3$
• Rotating and Orbiting Strings in Dp-brane background
• The Omega-Infinity Limit of Single Spikes
• P-Branes Dynamics, AdS/CFT and Correlation Functions
• Perturbations of giant magnons and single spikes in $\mathbb{R}\times S^2$
• Novel aspects of integrability for NLSMs in symmetric spaces