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arXiv 1302.6113hep-th
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高自旋AdS_3/CFT_2中四点函数的匹配

Matching four-point functions in higher spin AdS_3/CFT_2

Eliot Hijano, Per Kraus, Eric Perlmutter

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41 pages
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摘要：

在三维高自旋引力和二维W_N极小模型CFTs之间的对偶性的背景下，我们计算了一类体上和边界上的四点函数，并证明了它们之间的精确一致性.这是第一次在三维高自旋引力相关的计算，其功能形式是不固定的共形不变性。在大部分，我们使用优雅的方法来解决标量场方程，只使用矩阵操作，而在CFT方面，我们采用库仑气体表示。比较是在半经典极限，其中的中心荷采取无穷大在固定N。在此基础上，我们建立了高自旋引力下多道算子关联函数的计算规则。该方法涉及解决的标量主场方程的一般表示的散装规范代数。虽然我们的大部分工作是针对基于sl（N）× sl（N）的体理论进行的，但我们也讨论了我们的方法如何适用于hs[λ] × hs[λ]理论，这与't Hooft极限有关。

英文摘要：

Working in the context of the proposed duality between 3D higher spin gravity and 2D W_N minimal model CFTs, we compute a class of four-point functions in the bulk and on the boundary, and demonstrate precise agreement between them. This is the first computation of a correlator in 3D higher spin gravity whose functional form is not fixed by conformal invariance. In the bulk we make use of elegant methods to solve the scalar field equation using only matrix manipulations, while on the CFT side we employ the Coulomb gas representation. Comparison is made in the semiclassical limit, in which the central charge is taken to infinity at fixed N. Along the way, we establish the rules for computing correlation functions of multi-trace operators in higher spin gravity. The method involves solving the scalar master field equation in a general representation of the bulk gauge algebra. Although most of our work is carried out for the bulk theory based on sl(N) x sl(N), we also discuss how our methods can be adapted to the hs[λ] x hs[λ] theory, which is relevant in the 't Hooft limit.

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