Bum-Hoon Lee, Kamal L. Panigrahi, Chanyong Park
We study a giant magnon and a spike solution for the string rotating on AdS(4) X CP**3 geometry. We consider rigid rotating fundamental string in the SU(2) X SU(2) sector inside the CP**3 and find out the general form of all the conserved charges. We find out the dispersion relation corresponding to both the known giant magnon and the new spike solutions. We further study the finite size correction in both cases.
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We study rigidly rotating strings in $\varkappa$-deformed $AdS$ background. We probe this classically integrable background with `spiky' strings and analyze the string profiles in the large charge limit systematically. We also discuss the dispersion relation among the conserved charges for these solutions in long string limit.
We study rigidly rotating strings in the background of AdS3 x S3 with Neveu-Schwarz (NS) fluxes. We find two interesting limiting cases corresponding to the known giant magnon and the new single spike solution of strings in the above background and write down the dispersion relations among various conserved charges. We use proper regularization to find the correct relations among them. We further study the circular and infinite spiky strings on AdS and study their properties.
Using the reduction of the string sigma model to the 1-d Neumann integrable model we reconstruct the closed string solution with two equal spins in AdS_5 which is specified by the number of round arcs and one winding number. From the string sigma model itself as well as its reducion to the Neumann-Rosochatius system we construct a spiky string solution with two unequal spins in AdS_5 whose ratio is fixed and derive its energy-spin relation. The string configuration is characterized by the number of spikes and two equal winding numbers associated with the two rotating angular directions.
We discuss finite-size corrections to the spiky strings in $AdS$ space which is dual to the long $\mathcal{N}=4$ SYM operators of the form Tr($Δ_+ ^{J_1}ϕ_1Δ_+ ^{J_2}ϕ_2...Δ_+ ^{J_n}ϕ_n$). We express the finite-size dispersion relation in terms of Lambert $\mathbf{W}$-function. We further establish the finite-size scaling relation between energy and angular momentum of the spiky string in presence of mixed fluxes in terms of $\mathbf{W}$-function. We comment on the solution in pure NS-NS background as well.
We study rigidly rotating strings in $β$-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 $AdS_5 \times S_γ^5$.
We find a new class of spiky solutions for closed strings in flat, $AdS_3\subset AdS_5$ and $R\times S^2(\subset S^5)$ backgrounds. In the flat case the new solutions turn out to be T-dual configurations of spiky strings found by Kruczenski hep-th/0410226. In the case of solutions living in $AdS$, we make a semi classical analysis by taking the large angular momentum limit. The anomalous dimension for these dual spikes is similar to that for rotating and pulsating circular strings in AdS with angular momentum playing the role of the level number. This replaces the well known logarithmic depend…
We study general rotating string solution in the AdS(4) X CP**3 background with a B_NS holonomy turned on over ${\bf CP}^1$ $\subset $ $ {\bf CP}^3$. We find the giant magnon and single spike solutions for the string moving in this background corresponding to open spin chain. We calculate the corresponding dispersion relation among various conserved charges for both the cases. We further study the finite size effect on both the giant magnon and single spike solutions.
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-spik…
We consider semiclassical quantization of spiky strings spinning in AdS_3 part of AdS_5 X S^5 using integrability-based (algebraic curve) method. In the "short string" (small spin) limit the expansion of string energy starts with its flat-space expression. We compute the leading quantum string correction to "short" spiky string energy and find the explicit form of the corresponding 1-loop coefficient a_01. It turns out to be rational and expressed in terms of the harmonic sums as functions of the number n of spikes. In the special case of n=2 when the spiky string reduces to the single-folded …
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 $(B_{μν})$ and find out limiting cases corresponding to magnon and spike like solutions.
We determine spectral curves for the known spiky string solutions in AdS space in the limit of large angular momentum. We also construct generic multi-spike solutions in this limit and compute the corresponding spectral data. The resulting spectral curves precisely match those of the classical spin chain describing the dual operators in one-loop gauge theory. Our results confirm the map between string theory and gauge theory degrees of freedom proposed in arXiv:0805.4387 [hep-th].
We find explicit solutions for giant magnons and spiky strings on the squashed three dimensional sphere. For a special value of the squashing parameter the solutions describe strings moving in a sector of the conifold, while for another value of the squashing parameter we recover the known results on the round three dimensional sphere. A new feature is that the energy and the momenta enter in the dispersion relation of the conifold in a transcendental way.
The closed string dynamics in $\rr^{1,2}$ and $SL(2,\rr)$ is studied within the scheme of Pohlmeyer reduction. In both spaces two different classes of string surfaces are specified by the structure of the fundamental quadratic forms. The first class in $\rr^{1,2}$ is associated with the standard lightcone gauge strings and the second class describes spiky strings and their conformal deformations on the Virasoro coadjoint orbits. These orbits correspond to singular Liouville fields with the monodromy matrixes $\pm I$. The first class in $SL(2,\rr)$ is parameterized by the Liouville fields with …
We study spiky string solutions in AdS3 x S1 that are characterized by two spins S,J as well as winding m in S1 and spike number n. We construct explicitly two-cut solutions by using the SL(2) asymptotic Bethe Ansatz equations at leading order in strong coupling. Unlike the folded spinning string, these solutions have asymmetric distributions of Bethe roots. The solutions match the known spiky string classical results obtained directly from string theory for arbitrary semiclassical parameters, including J=0 and any value of S, namely short and long strings. At large spins and winding number th…
We study solutions for a rotating string on S^3 with a background NS-NS B-field and show the existence of spiky string and giant magnon as two limiting solutions. We make a connection to the sine-Gordon model via the Polyakov worldsheet action and study the effect of B-field. In particular, we find the magnon solution can be mapped to the excitation of a fractional spin chain. We conjecture a B-deformed SYM to be the gauge theory dual to this background.
Perturbations of a class of semiclassical spiky strings in three dimensional Anti-de Sitter (AdS) spacetime, are investigated using the well-known Jacobi equations for small, normal deformations of an embedded timelike surface. We show that the equation for the perturbation scalar which governs the behaviour of such small deformations, is a special case of the well-known Darboux-Treibich-Verdier (DTV) equation. The eigenvalues and eigensolutions of the DTV equation for our case are obtained by solving certain continued fractions numerically. These solutions are thereafter utilised to further d…
We study rigidly rotating strings in the near horizon geometry of the 1+1 dimensional intersection of two orthogonal stacks of NS5-branes, the so called I-brane background. We solve the equations of motion of the fundamental string action in the presence of two form NS-NS fluxes that the I-brane background supports and write down general form of conserved quantities. We further find out two limiting cases corresponding to giant magnon and single spike like strings in various parameter space of solutions.
We construct semi-classical string solutions of the Schrödinger $Sch_5 \times S^5$ spacetime, which is conjectured to be the gravity dual of a non-local dipole-deformed CFT. They are the counterparts of the giant magnon and spiky string solutions of the undeformed $AdS_5 \times S^5$ to which they flow when the deformation parameter is turned off. They live in an $S^3$ subspace of the five-sphere along the directions of which the $B$-field has non-zero components having also extent in the $Sch_5$ part of the metric. Finally, we speculate on the form of the dual field theory operators.
We study spiky strings in the context of the SL(2) Bethe ansatz equations. We find an asymmetric distribution of Bethe roots along one cut that determines the all loop anomalous dimension at leading and subleading orders in a large S expansion. At leading order in strong coupling (large lambda) we obtain that the energy of such states is given, in terms of the spin S and the number of spikes n by E-S=n sqrt{lambda}/(2 pi) (ln 16 pi S/(n sqrt{lambda})+ ln sin (pi/n) - 1)+ O(ln S/S). This result matches perfectly the same expansion obtained from the known spiky string classical solution. We then…
We study rigid string solutions rotating on the S^3 subspace of the beta-deformed AdS_5xS^5 background found by Lunin and Maldacena. For particular values of the parameters of the solutions we find the known giant magnon and single spike strings. We present a single spike string solution on the deformed S^3 and find how the deformation affects the dispersion relation. The possible relation of this string solution to spin chains and the connection of the solutions on the undeformed S^3 to the sine-Gordon model are briefly discussed.
We analyse semiclassical strings in AdS in the limit of one large spin. In this limit, classical string dynamics is described by a finite number of collective coordinates corresponding to spikes or cusps of the string. The semiclassical spectrum consists of two branches of excitations corresponding to "large" and "small" spikes respectively. We propose that these states are dual to the excitations known as large and small holes in the spin chain description of N=4 SUSY Yang-Mills. The dynamics of large spikes in classical string theory can be mapped to that of a classical spin chain of fixed l…
Perturbations of a class of semiclassical strings known today as spiky strings, are studied using the well-known Jacobi equations for small normal deformations of an embedded timelike surface. It is shown that there exists finite normal perturbations of the spiky string worldsheets embedded in a $2+1$ dimensional flat spacetime. Such perturbations lead to a rounding off of the spikes, which, in a way, demonstrates the stable nature of the unperturbed worldsheet. The same features appear for the dual spiky string solution and in the spiky as well as their dual solutions in $3+1$ dimensional fla…
Recently, classical solutions for strings moving in AdS5 x S5 have played an important role in understanding the AdS/CFT correspondence. A large set of them were shown to follow from an ansatz that reduces the solution of the string equations of motion to the study of a well-known integrable 1-d system known as the Neumann-Rosochatius (NR) system. However, other simple solutions such as spiky strings or giant magnons in S5 were not included in the NR ansatz. We show that, when considered in the conformal gauge, these solutions can be also accomodated by a version of the NR-system. This allows …
We first focus on the finite-gap formalism for type IIB strings in AdS_3 x S^1, which allows to encode the semiclassical spectrum of a very large family of string solutions in a Riemann surface, the spectral curve. Then, we show that, in the large angular momentum limit, it separates into two distinct surfaces, allowing the derivation of an explicit expression for the spectrum, which is correspondingly characterised by two separate branches. The latter may be interpreted in terms of two kinds of spikes appearing on the strings: "large" spikes, yielding an infinite contribution to the energy an…
We consider rigid rotating closed strings with spikes in AdS5 dual to certain higher twist operators in N=4 SYM theory. In the limit of large spin when the spikes reach the boundary of AdS5, the solutions with different numbers of spikes are related by conformal transformations, implying that their energy is determined by the same function of the `t Hooft coupling f(lambda) that appears in the anomalous dimension of twist 2 operators or in the cusp anomaly. In the limit when the number of spikes goes to infinity, we find an equivalent description in terms of a string moving in an AdS pp-wave b…
We study semiclassical spiky strings in de Sitter space and the corresponding Regge trajectories, generalizing the analysis in anti-de Sitter space. In particular we demonstrate that each Regge trajectory has a maximum spin due to de Sitter acceleration, similarly to the folded string studied earlier. While this property is useful for the spectrum to satisfy the Higuchi bound, it makes a nontrivial question how to maintain mildness of high-energy string scattering which we are familiar with in flat space and anti-de Sitter space. Our analysis implies that in order to have infinitely many highe…
In this paper, rotating strings in three directions of $AdS_4 \times \mathbb{CP}^3$ geometry are studied; its divergent energy limit, and conserved charges are also determined. An interpretation of these configurations as either giant magnons or spiky strings are discussed.
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 correspondi…
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 dependenc…
In this paper, novel solutions for strings with three angular momenta in $AdS_5 \times S^5$ geometry are presented; the divergent energy limit and the corresponding conserved charges, as well as dispersion relation are also determined. Interpretations of these configurations as either a giant magnon (GM) or a spiky string (SS) are discussed.
We construct a general class of solutions for a classical string in AdS_3 spacetime. The construction is based on a Pohlmeyer type reduction, with the sinh-Gordon model providing the general N-soliton solutions. The corresponding exact spiky string configurations are then reconstructed through the inverse scattering method. It is shown that the string moduli are determined entirely by those of the solitons.
We study rigidly rotating strings in AdS5 X S5 background with one spin along AdS5 and three angular momenta along S5. We find dispersion relations among various charges and interpret them as giant magnon and spiky string solutions in various limits. Further we present an example of oscillating string which oscillates in the radial direction of the AdS5 and at the same time rotates in S5.
Semiclassical spinning string states in AdS_5 are, in general, characterised by the three SO(2,4) conserved charges: the energy E and the two spins S_1 and S_2. We discuss several examples of explicit classical solutions for rigid closed strings of (bended) circular shape with two non-zero spins. In particular, we identify a solution that should represent a state that has minimal energy for large values of the two equal spins. Similarly to the spiky string in AdS_3, in the large spin limit this string develops long "arcs" that stretch towards the boundary of AdS_5. This allows the string to in…
In this paper, we study the spin chain and string excitation in the rotating Rindler-$AdS_3$ proposed in [12]. We obtain a one-parameter deformed $SL(2)$ spin chain at the fast spin limit. Two-spin GKP-like solutions are studied at short and long string limits. General ansatz for the giant magnons and the spiky strings are analyzed in detail for various $β$. At last, we explore its counterpart in analytic continuation and pp-wave limit.
We use Dirac-Born-Infeld action to study the spinning D-string in $AdS_3 $ background in the presence of both NS-NS and RR fluxes. We compute the scaling relation between the energy (E) and spin (S) in the `long string limit'. The energy of these spiky string is found to be a function of spin with the leading logarithmic behaviour and the scaling relation appears to be independent of the amount of flux present. We further discuss folded D-string solutions in $AdS_3$ background with pure NS-NS and R-R fluxes.
We use the recipe of arXiv:1003.2974 to find half-BPS near-horizon geometries in the t$^3$ model of $N=2$, $D=4$ gauged supergravity, and explicitely construct some new examples. Among these are black holes with noncompact horizons, but also with spherical horizons that have conical singularities (spikes) at one of the two poles. A particular family of them is extended to the full black hole geometry. Applying a double-Wick rotation to the near-horizon region, we obtain solutions with NUT charge that asymptote to curved domain walls with AdS$_3$ world volume. These new solutions may provide in…
By applying the conformal SO(2,4) transformations to the folded rotating string configuration with two spins given by a certain limit from the helical string solution in AdS_3 x S^1, we construct new string solutions whose energy-spin relations are characterized by the boost parameter. When two SO(2,4) transformations are performed with two boost parameters suitably chosen, the straight folded rotating string solution with one spin in AdS_3 is transformed in the long string limit into the long spiky string solution whose expression is given from the helical string solution in AdS_3 by making a…
We construct self-dual string soliton solutions in $AdS_4\times S^7$ spacetime, starting from the covariant equations of motion of M5-brane. We study the properties of the solutions and find that their action are linearized, indicating the BPS nature of the solutions, and they have the same electric and magnetic charge. The straight string soliton solution represents the configuration of the membranes ending on M5-brane with a straight string intersection, and it behaves like the spiky solution in flat spacetime. The spherical string soliton solution, which could be related to the straight one…
The string sigma model in $AdS_3\times S^3$ supported by mixed three-form fluxes has recently been proved to be integrable which led to a plethora of work in this background including proposals for S matrix and study of semiclassical string profiles. Motivated by this, in this paper, we present a study of `spiky' strings in this background. We analyze the string profiles in detail and also find the dispersion relation between the charges in the `long' string limit after solving the equations of motion perturbatively upto the leading order in the Neveu-Schwarz flux $b$. We find that the dispers…
Strings on $AdS_3 \times S^3\times S^3\times S^1$ with mixed flux exhibit exact integrability. We wish to construct an integrable Neumann-Rosochatius (NR) model of strings starting with the type IIB supergravity action in $AdS_3 \times S^3\times S^3\times S^1$ with pure NSNS flux. We observe that the forms of the Lagrangian and the Uhlenbeck integrals of motion of the considered system are NR-like with some suitable deformations which eventually appear due to the presence of flux. We utilize the integrable framework of the deformed NR model to analyze rigidly rotating spiky strings moving only…
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 connecti…
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.
We review the semiclassical analysis of strings in AdS5xS5 with a focus on the relationship to the underlying integrable structures. We discuss the perturbative calculation of energies for strings with large charges, using the folded string spinning in an AdS3 subset of AdS5 as our main example. Furthermore, we review the perturbative light-cone quantization of the string theory and the calculation of the worldsheet S-matrix.
Recently important classes of solitonic string solutions were obtained - giant magnons and single spikes. In previous study we showed the existence of giant magnon-like membrane solutions and studied their properties. In this paper we investigate classical rotating membranes representing analog of a specific class of string spiky solutions. Using the reduction to the Neumann-Rosochatius integrable system we find analog of the string single spike solutions. In contrast to the magnon-like solutions, this case is characterized with finite difference of energy and ``winding number'' and finite spi…
We review basic examples of classical string solutions in AdS5xS5. We concentrate on simplest rigid closed string solutions of circular or folded type described by integrable 1-d Neumann system but mention also various generalizations and related open-string solutions.
We study the spectrum of open strings on AdS_2 branes in AdS_3 in an NS-NS background, using the SL(2,R) WZW model. When the brane carries no fundamental string charge, the open string spectrum is the holomorphic square root of the spectrum of closed strings in AdS_3. It contains short and long strings, and is invariant under spectral flow. When the brane carries fundamental string charge, the open string spectrum again contains short and long strings in all winding sectors. However, branes with fundamental string charge break half the spectral flow symmetry. This has different implications fo…
We examine the thermodynamics and stability of 5-dimensional flat anti-de Sitter (AdS) black strings, locally asymptotically anti-de Sitter spacetimes whose spatial sections are AdS black holes with Ricci flat horizons. We find that there is a phase transition for the flat AdS black string when the AdS soliton string is chosen as the thermal background. We find that this bulk phase transition corresponds to a 4-dimensional flat AdS black hole to AdS soliton phase transition on the boundary Karch-Randall branes. We compute the possibility of a phase transition from a flat AdS black string to a …
In this paper, we investigate the semiclassical strings in AdS(3)XS^2, in which the string configuration of AdS(3) is classified to three cases depending on the parameters. Each of these has a different anomalous dimension proportional to logS, S^(1/3) and S, where S is a angular momentum on AdS(3). Further we generalize the dispersion relations for various string configuration on AdS(3)XS^2.
We review the recent developements in the stability problem and phase diagram for asymptotically locally $AdS$ black strings. First, we quickly review the case of locally flat black string before turning to the case of locally $AdS$ spacetimes.
The equation of motion of test particles in the geometry of a black string embedded in a 5-dimensional AdS spacetime is studied.
String backgrounds of the form AdS_3 x N that give rise to two dimensional spacetime superconformal symmetry are constructed.
We study membrane configurations in AdS_{7/4}xS^{4/7}. The membranes are wrapped around the compact manifold S^{4/7} and are dynamically equivalent to bosonic strings in AdS_5. We thus conveniently identify them as "Stringy Membranes". For the case of AdS_7xS^4, their construction is carried out by embedding the Polyakov action for classical bosonic strings in AdS_5, into the corresponding membrane action. Therefore, every string configuration in AdS_5 can be realized by an appropriately chosen stringy membrane in AdS_7xS^4. We discuss the possibility of this being also the case for stringy me…
We describe the pure spinor string in the $AdS_5\times S^5$ using unconstrained matrices first used by Roiban and Siegel for the Green-Schwarz superstring.
The so called one-parameter (often called $\varkappa$) deformed $AdS$ string sigma models have attracted a lot of attention lately in the study of integrability in string theory. We construct various circular string solutions in the $(AdS_3 \times S^3)_{\varkappa}$ background and describe the characteristics of such solutions qualitatively. We study the Bohr-Sommerfeld like quantization for these string states to characterise the motion. Further we find a `long' string limit of such circular strings in the $\varkappa$-deformed $AdS_3$ and find a novel dependence of the oscillation number on th…
We present a study of the worldsheets that describe the classical limit of various string scattering processes. Our main focus is on string scattering in AdS spacetime because of its relation via the AdS/CFT correspondence to gluon scattering in {\cal N}=4 supersymmetric Yang-Mills theory. But we also consider analogous processes in flat Minkowski spacetime which we compare to the AdS case. In addition to scattering of string by string we also find and study worldsheets describing the scattering of a string by external sources.
We derive the energy of pulsating strings as a function of adiabatic invariant oscillation number, which oscillates in $S^2_{\varkappa}$. We find similar solutions for the strings oscillating in deformed $AdS_3$. Furthermore, we generalize the result to the oscillating strings in anti-de Sitter space in the presence of extra angular momentum in $(AdS_3 \times S^1)_\varkappa$.
We study segmented strings in flat space and in $AdS_3$. In flat space, these well known classical motions describe strings which at any instant of time are piecewise linear. In $AdS_3$, the worldsheet is composed of faces each of which is a region bounded by null geodesics in an $AdS_2$ subspace of $AdS_3$. The time evolution can be described by specifying the null geodesic motion of kinks in the string at which two segments are joined. The outcome of collisions of kinks on the worldsheet can be worked out essentially using considerations of causality. We study several examples of closed segm…
We review some applications of Type 0 string theory in the context of the AdS/CFT correspondence.
In this contribution we describe some soliton based techniques for generating classical AdS string solutions. The methods introduced are useful for further understanding of rotating AdS configurations with spikes which correspond to higher twist operators in SYM theory. The main identification (accomplished in arXiv:0712.1193) between solitons and string spikes is reviewed and extended. We describe how inverse scattering technique can be applied for reconstructing AdS string configurations from soliton solutions of sinh-Gordon theory (in the example of ${\rm AdS}_3$).
In this paper we generalize the results of arXiv:0806.4758 to non-zero value J of angular momentum in S^5. We compute the 1-loop correction to the energy of the folded spinning string in AdS_5 x S^5 in the particular limit of slow short string approximation. In this limit the string is moving in a near-flat central region of AdS_5 slowly rotating in both AdS_5 and S^5. The one-loop correction should represent the first subleading correction to strong coupling expansion of the anomalous dimension of short gauge theory operators of the form Tr D^S Z^J in the SL(2) sector.
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