Pulsating String Research Articles

Circular string in a black p-brane leading to chaos

We consider a pulsating string near a non-extremal black p-brane (p=5 and p=6) and investigate the chaos in the corresponding string dynamics by examining the Fast Lyapunov indicator(FLI) and Poincare section. In our system, the energy and the charge play the role of control parameters. For generic values of these parameters, the numerical results show that the dynamics primarily fall into three modes: capture, escape to infinity, and quasiperiodic depending on the initial location (near to or far away from the black brane horizon) of the string. Finally, probing for different values of the winding number (n) the dynamics turns out to be sensitive to n. In particular, we observe the point particle (n = 0) scenario to be integrable whereas at higher n the dynamics seems to be chaotic.

Neumann\u2013Rosochatius system for (m,n) string in AdS_3 times S^3 with mixed flux

SL(2,{mathbb {Z}}) invariant action for probe (m, n) string in AdS_3times S^3times T^4 with mixed three-form fluxes can be described by an integrable deformation of an one-dimensional Neumann–Rosochatius (NR) system. We present the deformed features of the integrable model and study general class of rotating and pulsating solutions by solving the integrable equations of motion. For the rotating string, the explicit solutions can be expressed in terms of elliptic functions. We make use of the integrals of motion to find out the scaling relation among conserved charges for the particular case of constant radii solutions. Then we study the closed (m, n) string pulsating in R_ttimes S^3. We find the string profile and calculate the total energy of such pulsating string in terms of oscillation number ({mathcal {N}}) and angular momentum ({mathcal {J}}).

Strings in Ramond-Ramond backgrounds from the Neveu-Schwarz-Ramond formalism

We treat RR flux backgrounds of type II string theory in the framework of closed superstring field theory based on the NSR formalism, focusing on two examples: (1) the pp-wave background supported by 5-form flux, and (2) AdS3 × S3 × M4 supported by mixed 3-form fluxes. In both cases, we analyze the classical string field solution perturbatively, and compute the correction to the dispersion relation of string states to quadratic order in the RR flux. In the first example, our result is in a delicate way consistent with that obtained from lightcone quantization of the Green-Schwarz string. In the second example, we will obtain numerically the mass corrections to pulsating type IIB strings in AdS3 × S3 × M4. Our results, valid at finite AdS radius, agree with previously known answers in the semiclassical limit and in the BMN limit respectively.

Neumann-Rosochatius system for strings in ABJ model

Neumann-Rosochatius system is a well known one dimensional integrable sys- tem. We study the rotating and pulsating string in AdS4× ℂℙ3 with a BNS holonomy turned on over ℂℙ1 ⊂ ℂℙ3, the so called Aharony-Bergman-Jafferis (ABJ) background. We observe that the string equations of motion in both cases are integrable and the Lagrangians reduce to a form similar to that of a deformed Neumann-Rosochatius system. We find out the scaling relations among various conserved charges and comment on the finite size effect for the dyonic giant magnons on Rt× ℂℙ3 with two angular momenta. For the pulsating string we derive the energy as function of oscillation number and angular momenta along ℂℙ3.

Perturbation of pulsating strings

We discuss semiclassical quantization of circular pulsating strings in text {AdS}_3 times text {S}^3 background with and without the Neveu-Schwarz–Neveu-Schwarz (NS–NS) flux. We find the equations of motion corresponding to the quadratic action in bosonic sector in terms of scalar quantities and invariants of the geometry. The general equations for studying physical perturbations along the string in an arbitrary curved spacetime are written down using covariant formalism. We discuss the stability of these string configurations by studying the solutions of the linearized perturbed equations of motion.

Spinning pulsating strings in (AdS_5 times S^5)_{varkappa }

We study a general class of spinning pulsating strings in (AdS_5 times S^5)_{varkappa } background. For these family of solitons, we examine the scaling relation between the energy, spin or angular momentum. We verify that in varkappa rightarrow 0 limit these relations reduce to the undeformed AdS_5 times S^5 case. We further study an example of a string which is spinning in the varkappa -deformed {hbox {AdS}}_5 and {hbox {S}}^5 simultaneously and find out the scaling relation among various conserved charges.

SL(2,\xa0Z) invariant rotating (m,\xa0n) strings in AdS_3times S^3 with mixed flux

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 the dyonic giant magnon and single spike solutions corresponding to the equations of motion of a probe string in this background and find various relationships among the conserved charges. We further study a class of pulsating (m, n) string in AdS_3 with mixed three form flux.

Tunnelling of pulsating strings in deformed Minkowski spacetime

Using the WKB approximation we analyse the tunnelling of a pulsating string in deformed Minkowski spacetime.

A note on oscillating strings in AdS3 × S 3 with mixed three-form fluxes

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.

Pulsating strings from two-dimensional CFT on [formula omitted

We propose a state from the two-dimensional conformal field theory on the orbifold (T4)N/S(N) as a dual description for a pulsating string moving in AdS3. We show that, up to first order in the deforming parameter, the energy in both descriptions has the same dependence on the mode number, but with a non-trivial function of the coupling.

THE STATIC STRING

In this paper, the quantum fluctuation of a rigid and static string is reported to be identical to a free quantum particle. Solutions similar to this static string have already been found in the semiclassical quantization of pulsating strings, and our results show that the semiclassical quantization of pulsating strings is, in some cases, a perturbation of static strings. We also interpret the energy of the static string as a lower bound for the pulsating string and speculate about a description of quantum mechanics in terms of semiclassical string theory.

On (non)integrability of classical strings in p-brane backgrounds

We investigate the question of possible integrability of classical string motion in curved p-brane backgrounds. For example, the D3-brane metric interpolates between the flat and the AdS5 × S5 regions in which string propagation is integrable. We find that while the point-like string (geodesic) equations are integrable, the equations describing an extended string in the complete D3-brane geometry are not. The same conclusion is reached for similar brane intersection backgrounds interpolating between flat space and AdSk × Sk. We consider, in particular, the case of the NS 5-brane—fundamental string background. To demonstrate non-integrability we make a special ‘pulsating string’ ansatz for which the string equations reduce to an effective one-dimensional system. Expanding near this simple solution leads to a linear differential equation for small fluctuations that cannot be solved in quadratures, implying non-integrability of the original set of string equations.

Pulsating strings in Lunin-Maldacena backgrounds

We consider pulsating strings in Lunin-Maldacena backgrounds, specifically in deformed Minkowski spacetime and deformed AdS_5xS^5. We find the relation between the energy and the oscillation number of the pulsating string when the deformation is small. Since the oscillation number is an adiabatic invariant it can be used to explore the regime of highly excited string states. We then quantize the string and look for such a sector. For the deformed Minkowski background we find a precise match with the classical results if the oscillation number is quantized as an even number. For the deformed AdS_5xS^5 we find a contribution which depends on the deformation parameter.

Open semiclassical strings and long defect operators in AdS/dCFT correspondence

We consider defect composite operators in a defect superconformal field theory obtained by inserting an ${\mathrm{AdS}}_{4}\ifmmode\times\else\texttimes\fi{}{\mathrm{S}}^{2}$-brane in the ${\mathrm{AdS}}_{5}\ifmmode\times\else\texttimes\fi{}{\mathrm{S}}^{5}$ background. The one-loop dilatation operator for the scalar sector is represented by an integrable open spin chain. We give a description to construct coherent states for the open spin chain. Then, by evaluating the expectation value of the Hamiltonian with the coherent states in a long operator limit, a Landau-Lifshitz type of sigma model action is obtained. This action is also derived from the string action and hence we find a complete agreement in both super Yang-Mills and string sides. We see that an $\mathrm{SO}(3{)}_{\mathrm{H}}$ pulsating string solution is included in the action and its energy completely agrees with the result calculated in a different method. In addition, we argue that our procedure would be applicable to other AdS-brane cases.

Semiclassical String Solutions on 1/2 BPS Geometries

We study semiclassical string solutions on the 1/2 BPS geometry of type IIB string theory characterized by concentric rings on the boundary plane. We consider both folded rotating strings carrying nonzero R-charge and circular pulsating strings. We find that unlike rotating strings, as far as circular pulsating strings are concerned, the dynamics remains qualitatively unchanged when the concentric rings replace AdS_5\times S^5. Using the gravity dual we have also studied the Wilson loop of the corresponding gauge theory. The result is qualitatively the same as that in AdS_5\times S^5 in the global coordinates where the corresponding gauge theory is defined on S^3\times R. We show that there is a correction to 1/L leading order behavior of the potential between external objects.

Semiclassical relativistic strings inS5and long coherent operators inN=4 SYM theory

We consider the low energy effective action corresponding to the 1-loop, planar, dilatation operator in the scalar sector of N=4 SU(N) SYM theory. For a general class of non-holomorphic ``long'' operators, of bare dimension L>>1, it is a sigma model action with 8-dimensional target space and agrees with a limit of the phase-space string sigma model action describing generic fast-moving strings in the S^5 part of AdS_5 x S^5. The limit of the string action is taken in a way that allows for a systematic expansion to higher orders in the effective coupling $\lambda/L^2$. This extends previous work on rigid rotating strings in S^5 (dual to operators in the SU(3) sector of the dilatation operator) to the case when string oscillations or pulsations in S^5 are allowed. We establish a map between the profile of the leading order string solution and the structure of the corresponding coherent, ``locally BPS'', SYM scalar operator. As an application, we explicitly determine the form of the non-holomorphic operators dual to the pulsating strings. Using action--angle variables, we also directly compute the energy of pulsating solutions, simplifying previous treatments.

Semi-classical string solutions for [formula omitted] SYM

We study semi-classically the dynamics of string solitons in the Maldacena–Nuñez background, dual in the infra-red to N=1 , d=4 SYM. For closed string configurations rotating in the S 2× R space wrapped by the stack of N D-branes we find a behaviour that indicates the decoupling of the stringy Kaluza–Klein modes with sufficiently large R-symmetry charge. We show that the spectrum of a pulsating string configuration in S 2 coincides with that of a N=2 super-sine-Gordon model. Closed string configurations spinning in the transversal S 3 give a relation of the energy and the conserved angular momentum identical to that obtained for configurations spinning in the S 5 of the AdS 5× S 5, dual to N=4 SYM. In order to obtain non-trivial relations between the energy and the spin, we also consider conical-like configurations stretching along a radial variable in the unwrapped directions of the system of D-branes and simultaneously along the transversal direction. We find that in this precise case, these configurations are unstable—contrary to other backgrounds, where we show that they are stable. We point out that in the Poincaré-like coordinates used for the Maldacena–Nuñez background it seems that it is not possible to reproduce the well-known field theory relation between the energy and the angular momentum. We reach a similar conclusion for the Klebanov–Strassler background, by showing that the conical-like configurations are also unstable.

Circular Semiclassical String solutions on Confining AdS/CFT Backgrounds

We study multiwrapped circular string pulsating in the radial direction of AdS black hole. We compute the energy of this string as a function of a large quantum number n. One then could associate it with energy and a quantum number of states in the dual finite temperature {\cal N}=4 SYM theory as well as three dimensional pure gauge theory. We observe that the n dependence of the energy has a universal form. We have also considered pulsating string in the background of the near-extremal D4-brane solution. Circular pulsating membrane in M-theory on AdS_7\times S^4 has also been studied.