标题： 尖峰弦与AdS/CFT对应关系 显示英文标题

标题： Spiky strings and the AdS/CFT correspondence

摘要： 我们首先关注IIB字符串在AdS_3 x S^1中的有限间隙形式，它允许将一个非常大的字符串解族的半经典谱编码在一个黎曼面上，即谱曲线。然后，我们表明，在大角动量极限下，它会分离成两个不同的曲面，从而可以推导出谱的显式表达式，该谱相应地由两个独立分支表征。后者可以解释为字符串上出现的两种类型的尖峰："大"尖峰，它们对字符串的能量和角动量产生无限贡献，而"小"尖峰则代表"大"尖峰背景上的有限激发。在AdS/CFT对偶的另一侧，我们考虑N=4超杨-米尔斯理论的sl(2)部分。相应的1环谱在大共形自旋极限下也编码在一个谱曲线上，并且用所谓的洞来表征。我们证明，通过适当的识别以及通过尖角反常维数描述的从弱到强't Hooft耦合的通常外推，规范理论和弦理论的大-S谱是一致的。此外，我们解释了如何将"小"洞和"大"洞与"小"尖峰和"大"尖峰对应起来。最后，我们讨论了AdS_3中几个显示有限间隙谱的显式尖峰弦解。我们在大S极限下计算它们的谱曲线，发现它们对应于有限间隙曲线模空间的特定区域。我们还解释了如何利用"大"尖峰从弦理论中提取离散的自由度系统，然后可以将其与对偶规范理论算符的自由度匹配，以及"小"尖峰实际上与生活在R x S^2中的巨磁子非常相似。 显示英文摘要

摘要： 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 and angular momentum of the string, and "small" spikes, representing finite excitations over the background of the "large" spikes. On the other side of the AdS/CFT correspondence, we consider the sl(2) sector of N=4 super Yang-Mills theory. The corresponding 1-loop spectrum, in the large conformal spin limit, is also encoded in a spectral curve and characterised in terms of the so-called holes. We show that, with the appropriate identifications and with the usual extrapolation from weak to strong 't Hooft coupling described by the cusp anomalous dimension, the large-S spectra of gauge theory and of string theory coincide. Furthermore, we explain how "small" and "large" holes may be identified with "small" and "large" spikes. Finally, we discuss several explicit spiky string solutions in AdS_3 which display the finite-gap spectrum. We compute their spectral curves in the large S limit, finding that they correspond to specific regions of the moduli space of the finite-gap curves. We also explain how "large" spikes may be used in order to extract a discrete system of degrees of freedom from string theory, which can then be matched with the degrees of freedom of the dual gauge theory operators, and how "small" spikes are in fact very similar to the Giant Magnons living in R x S^2.