Three Spin Spiky Strings in beta-deformed Background

We study rigidly rotating strings in $\beta$-deformed $AdS_5\times S^5$ background with one spin along AdS$_5$ and two angular momenta along $S^5$. We find the spiky string solutions and present the dispersion relation among various charges in this background. We further generalize the result to the case of four angular momenta along $AdS_5 \times S_{\gamma}^5$.Comment: 12 pages, minor corrections, added references, to appear in JHE

Generalized pulsating strings

In this paper we consider new solutions for pulsating strings. For this purpose we use tha idea of the generalized ansatz for folded and circular strings in hep-th/0311004. We find the solutions to the resulting Neumann-Rosochatius integrable system and the corrections to the energy. To do that we use the approach developed by Minahan in hep-th/0209047 and find that the corrections are quite different from those obtained in that paper and hep-th/0310188. We conclude with comments on our solutions and obtained corrections to the energy, expanded to the leading order in lambda.Comment: v.2 references added, citations corrected, 18 page

Spiky strings and single trace operators in gauge theories

We consider single trace operators of the form O_{m_1 ... m_n} = tr D_+^{m_1} F ... D_+^{m_n} F which are common to all gauge theories. We argue that, when all m_i are equal and large, they have a dual description as strings with cusps, or spikes, one for each field F. In the case of N=4 SYM, we compute the energy as a function of angular momentum by finding the corresponding solutions in AdS_5 and compare with a 1-loop calculation of the anomalous dimension. As in the case of two spikes (twist two operators), there is agreement in the functional form but not in the coupling constant dependence. After that, we analyze the system in more detail and find an effective classical mechanics describing the motion of the spikes. In the appropriate limit, it is the same (up to the coupling constant dependence) as the coherent state description of linear combinations of the operators O_{m_1 ... m_n} such that all m_i are equal on average. This agreement provides a map between the operators in the boundary and the position of the spikes in the bulk. We further suggest that moving the spikes in other directions should describe operators with derivatives other than D_+ indicating that these ideas are quite generic and should help in unraveling the string description of the large-N limit of gauge theories.Comment: 23 pages, 5 figures. v2: References and comments adde

Infinite spin limit of semiclassical string states

Motivated by recent works of Hofman and Maldacena and Dorey we consider a special infinite spin limit of semiclassical spinning string states in AdS5 x S5. We discuss examples of known folded and circular 2-spin string solutions and demonstrate explicitly that the 1-loop superstring correction to the classical expression for the energy vanishes in the limit when one of the spins is much larger that the other. We also give a general discussion of this limit at the level of integral equations describing finite gap solutions of the string sigma model and argue that the corresponding asymptotic form of the string and gauge Bethe equations is the same.Comment: 38 pages, 3 figures; v2: comments on derivation of bound states of magnons from discrete Bethe equations added in section 4 and appendix C, references added, Imperial-TP-AT-6-4, HUTP-06/A002

Folded Three-Spin String Solutions in AdS_5 x S^5

We construct a spinning closed string solution in AdS_5 x S^5 which is folded in the radial direction and has two equal spins in AdS_5 and a spin in S^5. The energy expression of the three-spin solution specified by the folding and winding numbers for the small S^5 spin shows a logarithmic behavior and a one-third power behavior of the large total AdS_5 spin, in the long string and in the short string located near the boundary of AdS_5 respectively. It exhibits the non-regular expansion in the 't Hooft coupling constant, while it takes the regular one when the S^5 spin becomes large.Comment: 14 pages, LaTeX, no figures, a reference adde

Neumann and Neumann-Rosochatius integrable systems from membranes on AdS_4xS^7

It is known that large class of classical string solutions in the type IIB AdS_5xS^5 background is related to the Neumann and Neumann-Rosochatius integrable systems, including spiky strings and giant magnons. It is also interesting if these integrable systems can be associated with some membrane configurations in M-theory. We show here that this is indeed the case by presenting explicitly several types of membrane embedding in AdS_4xS^7 with the searched properties.Comment: LaTeX, 17 pages, no figures;v2: comments and citations added;v3: 20 pages, new subsection, explanations, comments and references added; v4: some typos fixed, to appear in JHE

Giant Magnons under NS-NS and Melvin Fields

The giant magnon is a rotating spiky string configuration which has the same dispersion relation between the energy and angular momentum as that of a spin magnon. In this paper we investigate the effects of the NS-NS and Melvin fields on the giant magnon. We first analyze the energy and angular momenta of the two-spin spiky D-string moving on the $AdS_3\times S^1$ with the NS-NS field. Due to the infinite boundary of the AdS spacetime the D-string solution will extend to infinity and it appears the divergences. After adding the counter terms we obtain the dispersion relation of the corresponding giant magnon. The result shows that there will appear a prefactor before the angular momentum, in addition to some corrections in the sine function. We also see that the spiky profile of a rotating D-string plays an important role in mapping it to a spin magnon. We next investigate the energy and angular momentum of the one-spin spiky fundamental string moving on the $R \times S^2$ with the electric or magnetic Melvin field. The dispersion relation of the corresponding deformed giant magnon is also obtained. We discuss some properties of the correction terms and their relations to the spin chain with deformations.Comment: Latex 20 pages, mention D-string and add reference

Circular and Folded Multi-Spin Strings in Spin Chain Sigma Models

From the SU(2) spin chain sigma model at the one-loop and two-loop orders we recover the classical circular string solution with two S^5 spins (J_1, J_2) in the AdS_5 x S^5 string theory. In the SL(2) sector of the one-loop spin chain sigma model we explicitly construct a solution which corresponds to the folded string solution with one AdS_5 spin S and one S^5 spin J. In the one-loop general sigma model we demonstrate that there exists a solution which reproduces the energy of the circular constant-radii string solution with three spins (S_1, S_2, J).Comment: 16 pages, LaTeX, no figure

Operator with large spin and spinning D3-brane

We consider the conformal dimension of an operator with large spin, using a spinning D3-brane with electric flux in AdS_5 x S^5 instead of spinning fundamental string. This spinning D3-brane solution seems to correspond to an operator made by taking trace in a large symmetric representation. The conformal dimension, the spin and the R-charge show a scaling relation in a certain region of parameters. In the small string charge limit, the result is consistent with the fundamental string picture. There is a phase transition when the fundamental string charge become larger than a certain critical value; there is no stable D3-brane solution above the critical value.Comment: 16 pages, 4 figures. v2: typos corrected, references added, series expansion of anomalous dimension added. v3: a reference added, comment on calculation in gauge theor

Holographic three-point functions for short operators

We consider holographic three-point functions for operators dual to short string states at strong coupling in N=4 super Yang-Mills. We treat the states as point-like as they come in from the boundary but as strings in the interaction region in the bulk. The interaction position is determined by saddle point, which is equivalent to conservation of the canonical momentum for the interacting particles, and leads to conservation of their conformal charges. We further show that for large dimensions the rms size of the interaction region is small compared to the radius of curvature of the AdS space, but still large compared to the string Compton wave-length. Hence, one can approximate the string vertex operators as flat-space vertex operators with a definite momentum, which depends on the conformal and R-charges of the operator. We then argue that the string vertex operator dual to a primary operator is chosen by satisfying a twisted version of Q^L=Q^R, up to spurious terms. This leads to a unique choice for a scalar vertex operator with the appropriate charges at the first massive level. We then comment on some features of the corresponding three-point functions, including the application of these results to Konishi operators.Comment: 24 pages; v2: References added, typos fixed, minor change