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arXiv 1111.3926hep-th
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D=3高自旋引力中的标量场和三点函数

Scalar fields and three-point functions in D=3 higher spin gravity

Martin Ammon, Per Kraus, Eric Perlmutter

摘要:

在Vasiliev高自旋引力的AdS真空中,对任意形变参数λ,计算了包含两个标量和一个任意自旋的规范场的边界三点函数.在此过程中,我们开发了在任意高自旋背景下提取标量场方程的工具。我们将hs[λ] + hs[λ] Chern-Simons理论与标量场相耦合,有效地利用了hs[λ]代数的结合孤星积.我们的结果与CFT的预期完全一致,特别是与任何在大中心荷下具有W_{\infinity} [λ]对称性的CFT以及与标量场对偶的原算符的CFT的结果一致。由于这一结果包含了W_N极小模型CFT的`t Hooft极限,我们的结果进一步证明了这两个理论之间的AdS/CFT对偶性.

英文摘要:

We compute boundary three-point functions involving two scalars and a gauge field of arbitrary spin in the AdS vacuum of Vasiliev's higher spin gravity, for any deformation parameter λ. In the process, we develop tools for extracting scalar field equations in arbitrary higher spin backgrounds. We work in the context of hs[λ] + hs[λ] Chern-Simons theory coupled to scalar fields, and make efficient use of the associative lone-star product underlying the hs[λ] algebra. Our results for the correlators precisely match expectations from CFT; in particular they match those of any CFT with W_{\infinity}[λ] symmetry at large central charge, and with primary operators dual to the scalar fields. As this is expected to include the `t Hooft limit of the W_N minimal model CFT, our results serve as further evidence of the conjectured AdS/CFT duality between these two theories.

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