Classical/quantum integrability in AdS/CFT
Classical/quantum integrability in AdS/CFT
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DOI：
10.1088/1126-6708/2004/05/024
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发表时间：
2004-02
期刊：
影响因子：
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通讯作者：
V.A.Kazakov;A.Marshakov;J.A.Minahan;K.Zarembo
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文献类型：
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作者：
V.A.Kazakov;A.Marshakov;J.A.Minahan;K.Zarembo
从可积分系统的角度讨论了AdS/CFT对偶性，建立了N = 4超Yang-Mills中由两类标量场组成的单迹局部算子的维数与AdS 5 × s5中它们的对偶半经典弦态能量之间的直接关系。反常维数可以用一组贝特方程来计算，对于“长”算子，它可以简化为黎曼-希尔伯特问题。我们对长波长Bethe方程、经典铁磁体和SU(2)扇区中的经典弦解提出了统一的方法，并给出了一个由具有整周期亚纯微分的复杂曲线控制的一般解。利用这一解决方案，我们计算了这些长算子的反常维数，并证明了它们与弦理论的预测一致。
We discuss the AdS/CFT duality from the perspective of integrable systems and establish a direct relationship between the dimension of single trace local operators composed of two types of scalar fields in N = 4 super Yang-Mills and the energy of their dual semiclassical string states in AdS 5 × S 5 . The anomalous dimensions can be computed using a set of Bethe equations, which for “long” operators reduces to a Riemann-Hilbert problem. We develop a unified approach to the long wavelength Bethe equations, the classical ferromagnet and the classical string solutions in the SU (2) sector and present a general solution, governed by complex curves endowed with meromorphic differentials with integer periods. Using this solution we compute the anomalous dimensions of these long operators up to two loops and demonstrate that they agree with string-theory predictions.