Sigma model in $AdS_3\times S^3$ background supported by both NS-NS and R-R fluxes is one of the most distinguished integrable models. We study a class of classical string solutions for $N$-spike strings moving in $AdS_3 \times S^1$ with angular momentum $J$ in $S^1 \subset S^5$ in the presence of mixed flux. We observe that the addition of angular momentum $J$ or winding number $m$ results in the spikes getting rounded off and not end in cusp. The presence of flux shows no alteration to the rounding-off nature of the spikes. We also consider the large $N$-limit of $N$-spike string in $AdS_3 \times S^1$ in the presence of flux and show that the so-called Energy-Spin dispersion relation is analogous to the solution we get for the periodic-spike in $AdS_3-pp-$wave $\times S^1$ background with flux.
In this paper we study the solitonic string solutions of magnon and single spike type in the beta-deformed AdS_4 x CP3 background. We find the dispersion relations which are supposed to give the anomalous dimension of the gauge theory operators.
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.
In the string theory in AdS_4 \times CP^3 we construct the giant magnon and spike solutions with two spins in two kinds of subspaces of R_t \times CP^3 and derive the dispersion relations for them. For the single giant magnon solution in one subspace we show that its dispersion relation is associated with that of the big one-spin giant magnon solution in the RP^2 subspace. For the single giant magnon solution in the other complementary subspace its dispersion relation is similar to that of the one-spin giant magnon solution living in the S^2 subspace but has one additional spin dependence.
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…
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…
We study solutions for the rotating strings on the sphere with a background NS-NS field and on the Anti-de-Sitter spacetime. We show the existence of magnon and single spike solutions on R$\times$S$^2$ in the presence of constant magnetic field as two limiting cases. We also study the solution for strings on AdS$_3\times$ S$^3$ with Melvin deformation. The dispersion relations among various conserved charges are shown to receive finite corrections due to the deformation parameter. We further study the rotating string on AdS$_3 \times$ S$^3$ geometry with two conserved angular momenta on S$^3$ …
We generalize the one magnon solution in R X S^2 to unbounded M magnon and find the corresponding solitonic string configuration in the string sigma model. This configuration gives rise to the expected dispersion relation obtained from the spin chain model in the large 't Hooft coupling limit. After considering (M,M) multi-magnon or spike on R X S^2 X S^2 as a subspace of AdS(5)XS^5 or AdS(4)XCP^3, we investigate the dispersion relation and the finite size effect for (M,M) multi-magnon or spike.
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 ${\rm AdS}_3$).
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 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 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.
We study rigid string solutions rotating in $AdS_5\times S^5$ background. For particular values of the parameters of the solutions we find multispin solutions corresponding to giant magnons and single spike strings. We present an analysis of the dispersion relations in the case of three spin solutions distributed only in $S^5$ and the case of one spin in $AdS_5$ and two spins in $S^5$. The possible relation of these string solutions to gauge theory operators and spin chains are briefly discussed.
We use the reduction of the string dynamics on AdS_4 x CP^3 to the Neumann-Rosochatius integrable system. All constraints can be expressed simply in terms of a few parameters. We analyze the giant magnon and single spike solutions on R_t x CP^3 with two angular momenta in detail and find the energy-charge relations. The finite-size effects of the giant magnon and single spike solutions are analyzed.
We review some recent work and techniques for constructing dynamical string solutions in AdS spacetime. These solutions generalize the folded string and multi-spike solutions of GKP and Kruczenski. The methods developed for constructing these dynamical solutions are based on Pohlmeyer reduction to integrable sinh-Gordon type equations. The integrability of the equations is seen as the crucial tool for reconstruction of the string configurations. We discuss the physical meaning of these dynamical spike solutions and the question of their moduli space.
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.
In this paper we consider the finite size effects for the strings in β-deformed AdS_{5}\times T^{1,1} background. We analyze the finite size corrections for the cases of giant magnon and single spike string solution. The finite size corrections for the undeformed case are straightforwardly obtained sending the deformation parameter to zero.
Mixed-symmetry arbitrary spin massive, massless, and self-dual massive fields in AdS(5) are studied. Light-cone gauge actions for such fields leading to decoupled equations of motion are constructed. Light-cone gauge formulation of mixed-symmetry anomalous conformal currents and shadows in 4d flat space is also developed. AdS/CFT correspondence for normalizable and non-normalizable modes of mixed-symmetry AdS fields and the respective boundary mixed-symmetry anomalous conformal currents and shadows is studied. We demonstrate that the light-cone gauge action for massive mixed-symmetry AdS field…
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…
After considering a solitonic string moving in the Poincare $AdS$ and two-dimensional sphere, we calculate the two-point correlation function of magnon and spike in the semi-classical limit without any explicit solution. We also calculate the three-point correlation functions between two heavy and one light operators. We find that the coupling between two heavy and one light operators in the string side is the exactly same as one obtained from the gauge theory by using the RG analysis.
Free AdS(5) mixed-symmetry massless bosonic and fermionic gauge fields of arbitrary spins are described by using su(2,2) spinor language. Manifestly covariant action functionals are constructed and field equations are derived.
We explicitly construct the four and two fermion zero modes for the mixed-flux generalization of the Hofman-Maldacena giant magnon on two of the AdS$_3$ backgrounds with maximal amount of supersymmetry, AdS$_3 \times$S$^3 \times$T$^4$ and AdS$_3 \times$S$^3 \times$S$^3 \times$S$^1$. We also show how to get the $\mathfrak{psu}(1|1)^4$ and $\mathfrak{su}(1|1)^2$ superalgebras from the semiclassically quantized fermion zero modes.
We study the finite size effect of rigidly rotating and spinning folded strings in $(AdS_3\times S^3)_{\varkappa}$ background. We calculate the leading order exponential corrections to the infinite size dispersion relation of the giant magnon, and single spike solutions. For the spinning folded strings we write the finite size effect in terms of the known Lambert $W$-function.
We obtain explicit formulas for the eight bosonic and eight fermionic fluctuations around the mixed-flux generalization of the Hofman-Maldacena giant magnon on AdS$_3 \times$S$^3 \times$T$^4$ and AdS$_3 \times$S$^3 \times$S$^3 \times$S$^1$. As a check of our results, we confirm that the semiclassical quantization of these fluctuations leads to a vanishing one-loop correction to the magnon energy, as expected from symmetry based arguments.
Free mixed-symmetry arbitrary spin massive bosonic and fermionic fields propagating in AdS(5) are investigated. Using the light-cone formulation of relativistic dynamics we study bosonic and fermionic fields on an equal footing. Light-cone gauge actions for such fields are constructed. Various limits of the actions are discussed.
We study the mixed phase of charged AdS black hole and radiation when the total energy is fixed below the threshold to produce a stable charged black hole branch. The coexistence conditions for the charged AdS black hole and radiation are derived for the generic case when radiation particles carry charge. The phase diagram of the mixed phase is demonstrated for both fixed potential and charge ensemble. In the dual gauge picture, they correspond to the mixed phase of quark-gluon plasma~(QGP) and hadron gas in the fixed chemical potential and density ensemble respectively. In the nuclei and heav…
We study solutions for rigidly rotating strings on AdS$_4 \times$ CP$^3$ in the presence of $B_{\rm NS}$ holonomy turned on over $CP^1 \subset CP^3$. We construct general solutions for rotating strings with two and three angular momenta in $CP^3$ and discuss various limits corresponding to giant magnon and spike like solutions.
In the framework of light-cone gauge approach, bosonic and fermionic mixed-symmetry continuous-spin fields in AdS space and flat space are considered. For such fields, the light-cone gauge actions are found. Realization of relativistic symmetries of AdS and flat spaces on the continuous-spin fields is also presented. Simple realization of spin operators is found. With respect to vector variable entering the continuous-spin fields, the spin operators for the fields in flat space turn out to be first-order differential operators, while, for the the fields in AdS space, the spin operators are rea…
The $AdS_3\times S^3$ string sigma model supported both by NS-NS and R-R fluxes has become a well known integrable model, however a putative dual field theory description remains incomplete. We study the anomalous dimensions of twist operators in this theory via semiclassical string methods. We describe the construction of a multi-cusp closed string in conformal gauge moving in $AdS_3$ with fluxes, which supposedly is dual to a general higher twist operator. After analyzing the string profiles and conserved charges for the string, we find the exact dispersion relation between the charges in th…
We study rigidly rotating and pulsating $(m,n)$ strings in $AdS_3 \times S^3$ with mixed three form flux. The $AdS_3 \times S^3$ background with mixed three form flux is obtained in the near horizon limit of $SL(2,Z)$-transformed solution, corresponding to the bound state of NS5-branes and fundamental strings. We study the probe $(m,n)-$string in this background by solving the manifest $SL(2,Z)-$covariant form of the action. We find out the dyonic giant magnon and single spike solutions corresponding to the equations of motion of a probe string in this background and find out various relations…
We study the semiclassical spectrum of bosonic string theory on AdS_3 x S^1 in the limit of large AdS angular momentum. At leading semiclassical order, this is a subsector of the IIB superstring on AdS_5 x S^5. The theory includes strings with K spikes which approach the boundary in this limit. We show that, for all K, the spectrum of these strings exactly matches that of the corresponding operators in the dual gauge theory up to a single universal prefactor which can be identified with the cusp anomalous dimension. We propose a precise map between the dynamics of the spikes and the classical …
The problem of finding consistent cubic AdS interactions of massless mixed-symmetry higher-spin fields is recast into a system of partial differential equations that can be solved for given spins of the particles entering the cubic vertices. For simplicity, we consider fields with two families of indices for which some examples of interactions are explicitly discussed.
We determine the off-shell symmetry algebra and representations of Type IIB superstring theory on $AdS_3\times S^3 \times T^4$ with mixed R-R and NS-NS three-form flux. We use these to derive the non-perturbative worldsheet S matrix of fundamental excitations of the superstring theory. Our analysis includes both massive and massless modes and shows how turning on mixed three-form flux results in an integrable deformation of the S matrix of the pure R-R theory.
We use a Pohlmeyer type reduction to generate classical string solutions in AdS spacetime. In this framework we describe a correspondence between spikes in AdS_3 and soliton profiles of the sinh-Gordon equation. The null cusp string solution and its closed spinning string counterpart are related to the sinh-Gordon vacuum. We construct classical string solutions corresponding to sinh-Gordon solitons, antisolitons and breathers by the inverse scattering technique. The breather solutions can also be reproduced by the sigma model dressing method.
Cubic interactions between the simplest mixed-symmetry gauge field and gravity are constructed in anti-de Sitter (AdS) and flat backgrounds. Nonabelian cubic interactions are obtained in AdS following various perturbative methods including the Fradkin-Vasiliev construction, with and without Stueckelberg fields. The action that features the maximal number of Stueckelberg fields can be considered in the flat limit without loss of physical degrees of freedom. The resulting interactions in flat space are compared with a classification of vertices obtained via the antifield cohomological perturbati…
In this paper we discuss in detail the frame-like formulation of free bosonic massless higher-spin fields of general symmetry type in AdS(d), announced recently in hep-th/0311164, hep-th/0501108. Properties of gauge invariant and AdS covariant action functionals and their flat limits are carefully analyzed.
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.
We study the finite size effect of rigidly rotating strings and closed folded strings in $AdS_3\times S^3$ geometry with NS-NS B-field. We calculate the classical exponential corrections to the dispersion relation of infinite size giant magnon and single spike in terms of Lambert $\mathbf{W}-$function. We also write the analytic expression for the dispersion relation of finite size Gubser-Klebanov-Polyakov (GKP) string in the form of Lambert $\mathbf{W}-$function.
We present a detailed study of the pulsating string solutions in AdS3 x S3 supported by both RR and NS-NS fluxes. This background has recently been proved to be integrable. We find the dispersion relation between the energy, oscillation number and other conserved charges when the NS-NS flux turned on is small. We further discuss the fate of the string solutions in pure RR and NS-NS cases.
We present the full list of conserved currents built of two massless spinor fields in Minkowski space and their derivatives multiplied by Clifford algebra elements. The currents have particular mixed-symmetry type described by Young diagrams with one row and one column of arbitrary lengths and heights. Along with Yukawa-like totally antisymmetric currents the complete set of constructed currents exactly matches the spectrum of AdS mixed-symmetry fields arising in the generalized Flato-Fronsdal theorem for two spinor singletons. As a by-product, we formulate and study general properties of prim…
Free mixed-symmetry continuous-spin fields propagating in AdS(5) space and flat R(4,1) space are studied. In the framework of a light-cone gauge formulation of relativistic dynamics, we build simple actions for such fields. Realization of relativistic symmetries on space of light-cone gauge mixed-symmetry continuous-spin fields is also found. Interrelations between constant parameters entering the light-cone gauge actions and eigenvalues of the Casimir operators of space-time symmetry algebras are obtained. Using these interrelations and requiring that the field dynamics in AdS(5) be irreducib…
According to the AdS/CFT dictionary, perturbing the large N boundary theory by a relevant double-trace deformation of the form f O^2 corresponds in the bulk to imposing ``mixed'' boundary conditions for the field dual to O. In this note we address various aspects of this correspondence. The change c_{UV} - c_{IR} of the central charge between the UV ad IR fixed points is known from explicit calculations (hep-th/0210093, hep-th/0212138) to be exactly the same in the bulk and in the boundary theories. By comparing the appropriate bulk and boundary functional determinants, we give a simple ``kine…
We study rigidly rotating strings in the $\varkappa$-deformed $AdS_3 \times S^3$ background. We find out two classes of solutions corresponding to the giant magnon and single spike solutions of the string rotating in two $S^2_{\varkappa}$ subspace of rotations reduced along two different isometries. We verify that the dispersion relations reduce to the well known relation in the $\varkappa\rightarrow 0$ limit. We further study some oscillating string solutions in the $S^3_{\varkappa}$ subspace.
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.
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 consider different supersymmetric mixed boundary conditions for scalar and fermionic fields in $AdS_2$, searching for the dual description of a family of interpolating Wilson Loops in ABJM theory. The family, which interpolates between the bosonic 1/6 BPS loop and the 1/2 BPS loop, can be thought of as an exact marginal deformation in a defect CFT$_1$. Confronting this property against holographic correlators and vacuum energy corrections singles out a particular boundary condition which we propose as dual to the interpolating family of Wilson loops.
The key aspects of a gauge-invariant Lagrangian description of massive and massless half-integer higher-spin fields in AdS spaces with a two-row Young tableaux $Y(s_1,s_2)$ are presented in an unconstrained description, as well as in off-shell formulations with algebraic constraints, on the basis of BFV-BRST operators for non-linear operator superalgebras, encoding the initial conditions realized by constraints in a Fock space and extracting the higher-spin fields from unitary representations of the AdS group.
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…
A new infinite-size limit of strings in RxS2 is presented. The limit is obtained from single spike strings by letting by letting the angular velocity parameter omega become infinite. We derive the energy-momenta relation of omega-infinity single spikes as their linear velocity v-->1 and their angular momentum J-->1. Generally, the v-->1, J-->1 limit of single spikes is singular and has to be excluded from the spectrum and be studied separately. We discover that the dispersion relation of omega-infinity single spikes contains logarithms in the limit J-->1. This result is somewhat surprising, si…
We revisit the calculation of one-loop corrections to the partition functions of a string ending on a circular or straight line in type IIB string theory on $AdS_3\times S^3 \times T^4$ supported by a mixture of 3-form fluxes depending on a parameter $q$ (with $q=0$ being R-R and $q=1$ pure NS-NS cases). Correcting earlier results in the literature, we find that the partition function depends on $q$ only through rescaled tension $T= T_0/(1-q^2)$.
We find the Yangian symmetry underlying the integrability of type IIB superstrings on $AdS_3 \times S^3 \times S^3 \times S^1$ with mixed Ramond-Ramond and Neveu-Schwarz-Neveu-Schwarz flux. The abstract commutation relations of the Yangian are formulated via RTT realisation, while its matrix realisation is in an evaluation representation depending on the quantised coefficient of the Wess-Zumino term. The construction naturally encodes a secret symmetry of the worldsheet scattering matrix whose generators map different Yangian levels to each other. We show that in the large effective string ten…
We elaborate on the ambient space approach to boundary values of $AdS_{d+1}$ gauge fields and apply it to massless fields of mixed-symmetry type. In the most interesting case of odd-dimensional bulk the respective leading boundary values are conformal gauge fields subject to the invariant equations. Our approach gives a manifestly conformal and gauge covariant formulation for these fields. Although such formulation employs numerous auxiliary fields, it comes with a systematic procedure for their elimination that results in a more concise formulation involving only a reasonable set of auxiliari…
We compute the quantum information metrics of a thermal CFT on $\mathbb R^{1,1}$ perturbed by the scalar primary operators of conformal dimension $Δ=3,4,5,6$. In particular, we assume that the Hamiltonian of the mixed state commutes with each other and the temperature is fixed. Under these conditions, the evaluation is analogous to the pure state case. We also apply the method of [arXiv:1607.06519] to calculate the mixed state information metric for the scalar primary operator with conformal dimension $Δ=4$ holographically. We find an exact agreement between the two results in our approach.
We present some generalities of unfolded on-shell dynamics that are useful in analysing the BMV conjecture for mixed-symmetry fields in constantly curved backgrounds. In particular we classify the Lorentz-covariant Harish-Chandra modules generated from primary Weyl tensors of arbitrary mass and shape, and in backgrounds with general values of the cosmological constant. We also discuss the unfolded notion of local degrees of freedom in theories with and without gravity and with and without massive deformation parameters, using the language of Weyl zero-form modules and their duals.
The spectrum of superstring theory on the $AdS_5 \times S_5$ Ramond-Ramond background in tensionless limit contains integer and half-integer higher-spin fields subject at most to two-rows Young tableaux $Y(s_1,s_2)$. We review the details of a gauge-invariant Lagrangian description of such massive and massless higher-spin fields in anti-de-Sitter spaces with arbitrary dimensions. The procedure is based on the construction of Verma modules, its oscillator realizations and of a BFV-BRST operator for non-linear algebras encoding unitary irreducible representations of AdS group.
