Scattering of single spikes

We apply the dressing method to a string solution given by a static string wrapped around the equator of a three-sphere and find that the result is the single spike solution recently discussed in the literature. Further application of the method allows the construction of solutions with multiple spikes. In particular we construct the solution describing the scattering of two single spikes and compute the scattering phase shift. As a function of the dressing parameters, the result is exactly the same as the one for the giant magnon, up to non-logarithmic terms. This suggests that the single spikes should be described by an integrable spin chain closely related to the one associated to the giant magnons. The field theory interpretation of such spin chain however is still unclear.Comment: 17 pages, LaTeX, 2 figures. v2: References added, typos correcte

Spiky Strings on NS5-branes

We study rigidly rotating strings in the near horizon geometry of a stack of Neveu-Schwarz (NS) 5-branes. We solve the Nambu-Goto action of the fundamental string in the presence of a NS-NS two form $(B_{\mu\nu})$ and find out limiting cases corresponding to magnon and spike like solutions.Comment: 10 pages, to appear in PL

Single spike solutions for strings on S2 and S3

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.Comment: LaTeX, 20 pages, 3 figures. v2: Refs adde

Spiky strings in AdS_3 x S^1 and their AdS-pp-wave limits

We study a class of classical solutions for closed strings moving in AdS_3 x S^1 part of AdS_5 x S^5 with energy E and spin S in AdS_3 and angular momentum J and winding m in S^1. They have rigid shape with n spikes in AdS_3. We find that when J or m are non-zero, the spikes do not end in cusps. We consider in detail a special large n limit in which S ~ n^2, J ~ n, i.e. S >> J >> 1, with (E+S)/ n^2, (E-S)/ n, J/n, m/n staying finite. In that limit the spiky spinning string approaches the boundary of AdS_5. We show that the corresponding solution can be interpreted as describing a periodic-spike string moving in AdS_3 --pp-wave x S^1 background. The resulting expression for the string energy should represent a strong-coupling prediction for anomalous dimension of a class of dual gauge theory states in a particular thermodynamic limit of the SL(2) spin chain.Comment: 34 pages, 4 figures; v2: references added; v3: typos correcte

D-brane Description of New Open String Solutions in AdS(5)

In this paper we find D-brane descriptions of some of new open string solutions that were found in 0804.3438[hep-th]. These D5-brane and D3-brane configurations give gravitational dual descriptions of Wilson loops in some particular representations.Comment: 13 pages, references adde

Notes on Euclidean Wilson loops and Riemann Theta functions

The AdS/CFT correspondence relates Wilson loops in N=4 SYM theory to minimal area surfaces in AdS5 space. In this paper we consider the case of Euclidean flat Wilson loops which are related to minimal area surfaces in Euclidean AdS3 space. Using known mathematical results for such minimal area surfaces we describe an infinite parameter family of analytic solutions for closed Wilson loops. The solutions are given in terms of Riemann theta functions and the validity of the equations of motion is proven based on the trisecant identity. The world-sheet has the topology of a disk and the renormalized area is written as a finite, one-dimensional contour integral over the world-sheet boundary. An example is discussed in detail with plots of the corresponding surfaces. Further, for each Wilson loops we explicitly construct a one parameter family of deformations that preserve the area. The parameter is the so called spectral parameter. Finally, for genus three we find a map between these Wilson loops and closed curves inside the Riemann surface.Comment: 35 pages, 7 figures, pdflatex. V2: References added. Typos corrected. Some points clarifie

Surprises in the AdS algebraic curve constructions - Wilson loops and correlation functions

The algebraic curve (finite-gap) classification of rotating string solutions was very important in the development of integrability through comparison with analogous structures at weak coupling. The classification was based on the analysis of monodromy around the closed string cylinder. In this paper we show that certain classical Wilson loop minimal surfaces corresponding to the null cusp and qqbar potential with trivial monodromy can, nevertheless, be described by appropriate algebraic curves. We also show how a correlation function of a circular Wilson loop with a local operator fits into this framework. The latter solution has identical monodromy to the pointlike BMN string and yet is significantly different.Comment: 36 pages; v2: minor correction