The operator product expansion of /N=4 SYM and the 4-point functions of supergravity
The operator product expansion of /N=4 SYM and the 4-point functions of supergravity
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/N=4 SYM 算子积展开与超引力四点函数
DOI：
10.1016/s0550-3213(00)00523-x
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发表时间：
1999
期刊：
影响因子：
--
通讯作者：
L. Rastelli
中科院分区：
文献类型：
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作者：
E. D'hoker;S. Mathur;Alec Matusis;L. Rastelli
我们对通过 AdS/CFT 对偶性从超重力计算出的共形 4 点函数的结果进行了详细的算子乘积展开解释。我们证明，对于 AdSd+1 中的任意标量交换，直接通道极限中的所有幂奇异项完全匹配对偶于交换体场及其共形后代的算子 OPE 的相应贡献。受保护的 N =4 超杨米尔斯算子（根据 AdS5×S5 上的 IIB 超引力计算）的 4 点函数中的领先对数奇点被解释为 OPE 中出现的双迹乘积的 O (1/N2) 重正化效应。应用于算子 Oφ∼( tr F2+⋯) 和 OC∼( tr F F ̃ +⋯) 的 4 点函数，该分析导致预测双迹组合 [ OφOC] 和 [ OφOφ− OCOC] 在大 N 、大 gYM2N 极限中具有反常维数 −16/N2 。我们描述了双引力理论中 OPE 的几何图，包括幂奇异项和主导对数。我们对我们结果的几种可能的扩展发表评论。
We give a detailed Operator Product Expansion interpretation of the results for conformal 4-point functions computed from supergravity through the AdS/CFT duality. We show that for an arbitrary scalar exchange in AdSd+1all the power-singular terms in the direct channel limit exactly match the corresponding contributions to the OPE of the operator dual to the exchanged bulk field and of its conformal descendents. The leading logarithmic singularities in the 4-point functions of protected N =4 super-Yang–Mills operators (computed from IIB supergravity on AdS5×S5) are interpreted as O (1/N2) renormalization effects of the double-trace products appearing in the OPE. Applied to the 4-point functions of the operators Oφ∼( tr F2+⋯) and OC∼( tr F F ̃ +⋯) , this analysis leads to the prediction that the double-trace composites [ OφOC] and [ OφOφ− OCOC] have anomalous dimension −16/N2in the large N , large gYM2N limit. We describe a geometric picture of the OPE in the dual gravitational theory, for both the power-singular terms and the leading logarithms. We comment on several possible extensions of our results.