Holographic reconstruction of AdS exchanges from crossing symmetry
Holographic reconstruction of AdS exchanges from crossing symmetry
复制标题
从交叉对称性全息重建 AdS 交换
DOI：
10.1007/jhep08(2017)147
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发表时间：
2017
影响因子：
5.4
通讯作者：
Eric Perlmutter
中科院分区：
文献类型：
--
作者：
L. Alday;A. Bissi;Eric Perlmutter
在ADS/CFT的启发下，我们讨论了大N共形场论中的一个悬而未决的问题：给定一个单迹算符出现在标量初等O$$\数学{O}$$的O×O$\数学{O}\数学{O}$$OPE中，它对交叉对称所决定的真空四点函数OOOO$$\LEFT\LANGE\数学{OOOO}\Right\RANGE$$的总贡献是多少？我们用1/N导数阶的四维共形场论解决了这个问题，从全息的角度看，这提供了一种在AdS5中重建交叉对称的四点交换振幅的场论。我们的解的形式是恢复交叉方程的大自旋解，并补充交叉所需的有限自旋的修正。这种方法可以应用于任意扭曲τ和自旋S算符的交换，尽管它大大简化了偶数扭曲的算符交换，给出了显式结果。输出是用于交换所有双迹操作符Oon，ℓ$${\Left[\Mathcal{O}\Mathcal{O}\Right]}_{n，\ell}$$的OPE数据集。我们发现，双迹反常维γn，ℓ是ℓ的负、单调和凸函数，对于所有n和所有ℓ>；S，这构成了整体因果性和偶数自旋场经典动力学的全息签名。我们还发现双道反常维度与OPE系数之间的“导数关系”一般不成立，并在几种情况下导出了偏差的显式形式。最后，我们研究了γn，ℓ的大n极限，这与Regge和Bulk-Point域有关。
A bstractMotivated by AdS/CFT, we address the following outstanding question in large N conformal field theory: given the appearance of a single-trace operator in the O×O$$ \mathcal{O}\times \mathcal{O} $$ OPE of a scalar primary O$$ \mathcal{O} $$, what is its total contribution to the vacuum four-point function OOOO$$ \left\langle \mathcal{OOOO}\right\rangle $$ as dictated by crossing symmetry? We solve this problem in 4d conformal field theories at leading order in 1/N. Viewed holographically, this provides a field theory reconstruction of crossing-symmetric, four-point exchange amplitudes in AdS5. Our solution takes the form of a resummation of the large spin solution to the crossing equations, supplemented by corrections at finite spin, required by crossing. The method can be applied to the exchange of operators of arbitrary twist τ and spin s, although it vastly simplifies for even-integer twist, where we give explicit results. The output is the set of OPE data for the exchange of all double-trace operators OOn,ℓ$$ {\left[\mathcal{O}\mathcal{O}\right]}_{n,\ell } $$. We find that the double-trace anomalous dimensions γn,ℓ are negative, monotonic and convex functions of ℓ, for all n and all ℓ > s. This constitutes a holographic signature of bulk causality and classical dynamics of even-spin fields. We also find that the “derivative relation” between double-trace anomalous dimensions and OPE coefficients does not hold in general, and derive the explicit form of the deviation in several cases. Finally, we study large n limits of γn,ℓ, relevant for the Regge and bulk-point regimes.