We study the class of pulsating strings on AdS_4 x CP3. Using a generalized ansatz for pulsating string configurations we find new solutions of this class. Further we quasi-classically quantize the theory and obtain the first corrections to the energy. The latter, due to AdS/CFT correspondence, is supposed to give the anomalous dimensions of operators of the gauge theory dual N=6 Chern-Simons theory.
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 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 AdS$_5$ and S$^5$ simultaneously and find out the scaling relation among various conserved charges.
One of the most important problems in any conformal field theory is the calculation of three-point functions of primary operators. In this paper we provide explicit examples of correlators with two scalar operators in $\,{\cal N}=4$ super-Yang--Mills theory at large $N$, corresponding to pulsating semiclassical strings in AdS$_5\times S^5$, and an operator with small quantum numbers at strong coupling.
Exact computation of one-loop correction to energy of pulsating strings in AdS_5 x S^5
本文是arXiv：1001：4018的续篇，我们计算了AdS_5 x S^5中脉动弦解能量的单圈修正。我们证明了，对于刚性自旋弦椭圆解，脉动解的涨落算子也可以用单间隙Lame形式表示。脉动解的一个新的方面是其能量的单圈修正用二次波动算子的稳定角表示。我们明确地研究了相应的单圈能量的“短弦”极限，证明了“小”半经典弦的能量形式具有一定的普遍性。我们的结果有助于揭示对偶规范理论算符反常维数强耦合展开的结构。
We explore nonrelativistic (NR) pulsating string configurations over torsion Newton-Cartan (TNC) geometry having topology $ R \times S^2 $ and check the corresponding analytic integrability criteria following Kovacic's algorithm. In the first part we consider pulsating strings propagating over TNC geometry whose world-sheet theory is described by relativistic CFTs. We compute conserved charges associated with the $ 2D $ sigma model and show that the classical phase space corresponding to these NR pulsating string configurations is Liouvillian integrable. Finally, we consider nonrelativisitc sc…
According to AdS/CFT duality semi-classical strings in the Schrödinger spacetime is conjectured to be a holographic dual to dipole CFT. In this paper we consider pulsating strings in five-dimensional Schrödinger space times five-sphere. We have found classical string solutions pulsating entirely in the Schrödinger part of the background. We quantize the theory semi-classically and obtain the wave function of the problem. We have found the corrections to the energy, which by duality are supposed to give anomalous dimensions of certain operators in the dipole CFT.
The quest for extension of holographic correspondence to non-relativistic sectors naturally includes Schrödinger backgrounds and their field theory duals. In this paper we study the holography by probing the correspondence with pulsating strings. The case we consider is pulsating strings in five-dimensional Schrödinger space times five-torus $T^{1,1}$, which has as field theory dual a dipole CFT. First we find particular pulsating string solutions and then semi-classically quantize the theory. We obtain the wave function of the problem and thoroughly study the corrections to the energy, which …
On the pulsating strings in Sasaki-Einstein spaces
研究了AdS_5 x Y^{p，q}和AdS_5 x L^{p，q，r}中的脉动弦类.利用脉动弦组态的广义解，我们用Heun函数找到了该类的新解，并导出了AdS_5 x T^{1，1}的特殊情况，这在arXiv：1006.1539 [hep-th]中已经分析过.不幸的是，Heun函数的研究仍然很少，我们不能准经典地解释理论，并获得第一个修正的能量。由于AdS/CFT对应，后者可以给出规范理论对偶N=1超共形场论中算符的反常维数.
We discuss semiclassical quantization of circular pulsating strings in AdS3 x S3 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.
We propose a state from the two-dimensional conformal field theory on the orbifold $(T^4)^N/S(N)$ as a dual description for a pulsating string moving in $AdS_3$. 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.
Circular strings pulsating in $AdS_3 \times S^3 \times T^4$ with mixed R-R and NS-NS three-form fluxes can be described by an integrable deformation of the one-dimensional Neumann-Rosochatius mechanical model. In this article we find a general class of pulsating solutions to this integrable system that can be expressed in terms of elliptic functions. In the limit of strings moving in $AdS_{3}$ with pure NS-NS three-form flux, where the action reduces to the $SL(2,\mathbb{R})$ WZW model, we find agreement with the analysis of the classical solutions of the system performed using spectral flow b…
$SL(2,\mathbb{Z})$ invariant action for probe $(m,n)$ string in $AdS_3\times S^3\times T^4$ 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 ca…
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…
Integrability and Higher Loops in AdS/dCFT Correspondence
我们进一步研究了开半经典弦与长亏损算子之间的对应关系，这在我们以前的工作[hep-th/0410139]中已经讨论过。本文从Riemann曲面的观点出发，根据Minahan的论证，对SO（6）-> SO（3）_H x SO（3）_V的自发对称性破缺给出了一个解释.然后利用单切解的预解式的具体形式，在三圈水平上计算了开脉动弦的对偶算子的反常维数。在弦边，我们通过半经典分析得到了开弦脉动解的能量。这两个结果同意在两个循环的水平，但我们发现一个三圈的差异。
Neumann-Rosochatius system is a well known one dimensional integrable system. We study the rotating and pulsating string in $AdS_4 \times \mathbb{CP}^3$ with a $B_{\rm{NS}}$ holonomy turned on over $\mathbb{CP}^1 \subset \mathbb{CP}^3$, or 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 deformed Neuman-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…
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 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 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…
Conformal SO(2,4) Transformations for the Helical AdS String Solution
通过将共形SO（2，4）变换应用于由AdS_3 x S^1中的螺旋弦解给出的具有一定极限的双自旋折叠旋转弦构型，我们构造了新的弦解，其能量-自旋关系由boost参数表征.通过选取两个适当的boost参数，进行两次SO（2，4）变换，在长弦极限下，AdS_3中的单自旋直折叠旋转弦解被变换为长刺弦解，其表达式由AdS_3中的螺旋弦解通过模参数为1的限制给出.
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 study non-relativistic limit of AdS(5)xS(5) background and determine corresponding Newton-Cartan fields. We also find canonical form of the new non-relativistic string in this background and discuss its formulation in the uniform light-cone gauge.
