arXiv 1504.017372015-04hep-th

共形块的Eikonalization

Eikonalization of Conformal Blocks

A. Liam Fitzpatrick, Jared Kaplan, Matthew T. Walters, Junpu Wang

备注：: 32+17 pages, 6 figures; references added, discussion of eikonal limit clarified
发表信息：: JHEP 09 (2015) 019
DOI：: 10.1007/JHEP09(2015)019

摘要：

经典的场结构，如库仑势和史瓦西解，是由许多光自由度的t通道交换建立的。我们研究这种现象的CFT模拟，我们称之为“eikonalization”的共形块。我们证明了当算符$T$出现在OPE $\mathcal{O}(x) \mathcal{O}(0)$中时，大自旋$\ell$ Fock空间态$[TT \cdots T]_{\ell}$也出现在这个OPE中，并且具有可计算的系数.这些Fock空间状态在$\langle \mathcal{O} \mathcal{O} \mathcal{O} \mathcal{O} \rangle$相关器中的交换的总和建立了对偶AdS描述中的经典“$T$字段”。在某些限制下，所有Fock空间交换的总和可以表示为$\mathcal{O}$的4-pt相关器中单个$T$交换的指数。我们的结果对于系统化$1/\ell$微扰理论和简化大自旋OPE系数的计算是有用的。作为例子，我们得到了Fock空间共形块系数的前导$\log \ell$依赖性，并直接计算了最简单的“三重迹”算子的OPE系数。

英文摘要：

Classical field configurations such as the Coulomb potential and Schwarzschild solution are built from the t-channel exchange of many light degrees of freedom. We study the CFT analog of this phenomenon, which we term the `eikonalization' of conformal blocks. We show that when an operator $T$ appears in the OPE $\mathcal{O}(x) \mathcal{O}(0)$, then the large spin $\ell$ Fock space states $[TT \cdots T]_{\ell}$ also appear in this OPE with a computable coefficient. The sum over the exchange of these Fock space states in an $\langle \mathcal{O} \mathcal{O} \mathcal{O} \mathcal{O} \rangle$ correlator build the classical `$T$ field' in the dual AdS description. In some limits the sum of all Fock space exchanges can be represented as the exponential of a single $T$ exchange in the 4-pt correlator of $\mathcal{O}$. Our results should be useful for systematizing $1/\ell$ perturbation theory in general CFTs and simplifying the computation of large spin OPE coefficients. As examples we obtain the leading $\log \ell$ dependence of Fock space conformal block coefficients, and we directly compute the OPE coefficients of the simplest `triple-trace' operators.

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