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arXiv 1306.0336hep-thgr-qc
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双迹流与全息RG的dS/CFT对应

Double Trace Flows and Holographic RG in dS/CFT correspondence

Diptarka Das, Sumit R. Das, Gautam Mandal

备注：
18 pages, no figures; (v2) minor typos fixed, references added
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摘要：

如果存在dS/CFT对应关系，则本体中的时间演化应转化为对偶欧几里德场论中的RG流。因此，虽然对偶场预计是非幺正的，但其RG流将在整体上携带幺正时间演化的印记。在这篇文章中，我们研究了在德西特空间中的全息RG的预测，用于任何建议的对偶中的双重和三重迹耦合的流动。我们显示相当一般的正确形式的场论β函数的双迹耦合是从全息获得的，提供一个标识的规模的场论与（i |T|），其中T是“时间”在共形坐标。对于dS（4），我们发现，通过适当选择算子归一化，有可能具有实n点关联函数以及具有实系数的beta函数。这种选择导致RG流的IR固定点在负耦合，不像在一个单一的理论，其中的IR固定点是在正耦合。所提出的Sp（N）矢量模型与de Sitter Vasiliev引力的对应提供了这种现象的一个具体例子。对于dS（d+1）与偶数d，然而，我们发现，没有选择的运营商规范化存在，这确保现实的系数的β函数，以及不存在的n个相关的阶段，为各种n点的功能，只要一个假设真正的耦合常数在散装拉格朗日。

英文摘要：

If there is a dS/CFT correspondence, time evolution in the bulk should translate to RG flows in the dual euclidean field theory. Consequently, although the dual field is expected to be non-unitary, its RG flows will carry an imprint of the unitary time evolution in the bulk. In this note we examine the prediction of holographic RG in de Sitter space for the flow of double and triple trace couplings in any proposed dual. We show quite generally that the correct form of the field theory beta functions for the double trace couplings is obtained from holography, provided one identifies the scale of the field theory with (i|T|) where T is the `time' in conformal coordinates. For dS(4), we find that with an appropriate choice of operator normalization, it is possible to have real n-point correlation functions as well as beta functions with real coefficients. This choice leads to an RG flow with an IR fixed point at negative coupling unlike in a unitary theory where the IR fixed point is at positive coupling. The proposed correspondence of Sp(N) vector models with de Sitter Vasiliev gravity provides a specific example of such a phenomenon. For dS(d+1) with even d, however, we find that no choice of operator normalization exists which ensures reality of coefficients of the beta-functions as well as absence of n-dependent phases for various n-point functions, as long as one assumes real coupling constants in the bulk Lagrangian.

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