We consider leading strong coupling corrections to the energy of the lightest massive string modes in AdS_5 x S^5, which should be dual to members of the Konishi operator multiplet in N=4 SYM theory. This determines the general structure of the strong-coupling expansion of the anomalous dimension of the Konishi operator. We use 1-loop results for several semiclassical string states to extract information about the leading coefficients in this expansion. Our prediction is
Delta= 2 lambda^{1/4} + b_0 + b_1 lambda^{-1/4} + b_3 lambda^{-3/4} +..., where b_0 and b_1 are rational while b_3 is transcendental containing zeta(3). Explicitly, we argue that b_0= Delta_0 - 4 (where Delta_0 is the canonical dimension of the corresponding gauge-theory operator in the Konishi multiplet) and b_1=1. Our conclusions are sensitive to few assumptions, implied by a correspondence with flat-space expressions, on how to translate semiclassical quantization results into predictions for the exact quantum string spectrum.
Semiclassical string computation of strong-coupling corrections to dimensions of operators in Konishi multiplet
在arXiv:0906.4294中的工作之后,我们展示了如何使用半经典弦量子化方法来计算AdS_5 x S^5弦态在第一激发弦能级上的能量的主要修正,这些修正应该对应于N=4 SYM理论的Konishi多重态中的算子。与前一篇文章中的例子相比,我们在这里考虑的弦解带有S^5角动量J的额外分量,这便于它们与小西多重态中的算符相鉴别。我们证明,对于J=2的弦态,在能量的大弦张力展开中,子前导λ ^(-1/4)项的系数是arXiv:0906.4294中发现的系数的两倍。由此得到的值与Y系统/TBA方法在sl(2)扇区中为小西状态找到的值相匹配,解决了之前声称的明显分歧。
Quantum folded string in S^5 and the Konishi multiplet at strong coupling
小西超共形多重态是一个重要的理论实验室,人们可以在这里测试AdS/CFT方法,以计算对AdS_5 x S^5超弦谱的强耦合修正。特别地,可以利用有限电荷状态/算子的可积性。多重态基态是在N=4的超Yang-Mills理论的秩1扇区sl(2)和su(2)中具有两个简单后代的单重态算符。最近,对sl(2)态的次领先量子修正已经被计算出来。在这里,我们使用代数曲线的方法来确定对其他状态的校正,恢复多重态内校正的普适性。
We review some recent progress in understanding the spectrum of energies/dimensions of strings/operators in AdS5 x S5 -- planar N=4 super Yang-Mills correspondence. We consider leading strong coupling corrections to the energy of lightest massive string modes in AdS5 x S5, which should be dual to members of the Konishi operator multiplet in the SYM theory. This determines the general structure of strong-coupling expansion of the anomalous dimension of the Konishi operator. Following arXiv:0906.4294 we use 1-loop results for semiclassical string states to extract information about the leading c…
Spectrum and Quantum Symmetries of the ${\rm AdS}_5 \times {\rm S}^5$ Superstring
${\cal N}=4$ SYM和AdS $_5\times\;$ S $^5$超弦之间的对偶性似乎在平面极限下享有量子可积性,这使得设计出表面上解决谱问题的强大方法成为可能。然而,AdS $_5\times\;$ S $^5$超弦的第一性原理量子化仍然是一个未解决的问题,特别是短弦态的谱以前只在大的t Hooft耦合中导出过。在这篇论文中,我们研究了将短弦态微扰量子化到首阶之外的可能途径,同样我们的目标是更好地理解量子对称性。一个突出的作用是由最低激发弦状态,对偶的小西超多重态,我们开始批判性地回顾一个断言的推导小西异常尺寸的设置纯旋弦论。其次,我们研究了静态规范下玻色子AdS $_5\times\;$ S $^5$弦,构造了一个所谓的单模弦解,它在量子水平上表现出在等距SO(2,4)$\;\times\;$ SO(6)下的经典可积性和不变性。论证了超对称性的影响,我们确实恢复了第一个非平凡的量子修正小西异常尺寸。我们继续实施静态规范的完整的AdS $_5\times\;$ S $^5$超弦,并找到优雅的拉格朗日密度和超荷的表达式。然后,我们限制我们的兴趣的超粒子,并使用两种不同的方法,在费米子的二次阶找到正则坐标。由于单模弦就是脉动弦的SO(2,4)$\;\times\;$ SO(6)轨道,我们得出结论:用轨道方法量子化玻色子AdS $_3\times\;$ S $^3$中的粒…
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 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.
Spinning strings in AdS_5 x S^5: A worldsheet perspective
我们研究了领先的Regge弦状态相关的半经典自旋弦的解决方案。利用初等RNS技术,构造了描述具有五种形式通量的时空中的大质量NSNS弦的有效拉格朗日量中的二次项。然后我们研究了AdS_5 × S ^5的特殊情况,发现AdS的“能量”(E_0)与AdS的自旋(S)、球的自旋(J)和球的轨道角动量(\nabla_a \nabla^a)的关系。
$AdS_3$ string theory in the stringy regime $k=(R_{AdS}/\ell_{str})^2 < 1$ provides a laboratory for the study of holography in which both sides of AdS/CFT duality are under fairly good control. Worldsheet string theory is solvable, and for closed strings the dual spacetime CFT is a deformation of a symmetric product orbifold. Here we extend this construction to include open strings by adding a probe D-string, described semi-classically by an $AdS_2$ D-brane in $AdS_3$. The dual defect or boundary conformal field theory (BCFT) is again a deformed symmetric product, which now describes the Fock…