Loops in AdS from conformal field theory
Loops in AdS from conformal field theory
复制标题
来自共形场论的 AdS 中的循环
DOI：
--
复制
发表时间：
2016
期刊：
影响因子：
--
通讯作者：
Eric Perlmutter
中科院分区：
文献类型：
--
作者：
O. Aharony;L. Alday;A. Bissi;Eric Perlmutter
本文提出并证明了共形场论（CFT）交叉方程在AdS/CFT中的一个新用途：AdS中回路振幅的计算，全息CFT中非平面交叉器的对偶。AdS中的循环在很大程度上未被探索，主要是由于直接计算的技术困难。我们重新审视这个问题，并在两个独立的方式的双重1/N扩展的CFTs。第一个是展示如何显式求解交叉方程的第一次领先阶在1/N2，给定的领先阶的解决方案。这是作为自旋的逆幂的系统展开，到所有阶。这些展开式可以用图解表示，从而得到有限自旋的CFT数据。我们的第二种方法涉及梅林空间。我们展示了如何极性的四点，回路级梅林振幅的一部分，可以完全重建的领先的顺序数据。用这两种方法计算的反常尺寸一致。在AdS中的E44理论的情况下，我们的交叉解决方案再现了以前的单圈气泡图的计算。我们可以进一步推导AdS中的四点标量三角图，这是从未计算过的。在这个过程中，我们将展示如何解析地推导出异常尺寸梅林振幅与无限系列的极点，并讨论应用程序更复杂的情况下，如N$ mathcal{N} $$ = 4超杨-米尔斯理论。
A bstractWe propose and demonstrate a new use for conformal field theory (CFT) crossing equations in the context of AdS/CFT: the computation of loop amplitudes in AdS, dual to non-planar correlators in holographic CFTs. Loops in AdS are largely unexplored, mostly due to technical difficulties in direct calculations. We revisit this problem, and the dual 1/N expansion of CFTs, in two independent ways. The first is to show how to explicitly solve the crossing equations to the first subleading order in 1/N2, given a leading order solution. This is done as a systematic expansion in inverse powers of the spin, to all orders. These expansions can be resummed, leading to the CFT data for finite values of the spin. Our second approach involves Mellin space. We show how the polar part of the four-point, loop-level Mellin amplitudes can be fully reconstructed from the leading-order data. The anomalous dimensions computed with both methods agree. In the case of ϕ4 theory in AdS, our crossing solution reproduces a previous computation of the one-loop bubble diagram. We can go further, deriving the four-point scalar triangle diagram in AdS, which had never been computed. In the process, we show how to analytically derive anomalous dimensions from Mellin amplitudes with an infinite series of poles, and discuss applications to more complicated cases such as the N$$ mathcal{N} $$ = 4 super-Yang-Mills theory.