A derivation of AdS/CFT for vector models

A derivation of AdS/CFT for vector models
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矢量模型的 AdS/CFT 推导

DOI:
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发表时间:
2020
影响因子:
5.4
通讯作者:
Erez Y. Urbach
Erez Y. Urbach
中科院分区:
物理与天体物理2区
文献类型:
--
作者:
O. Aharony;Shai M. Chester;Erez Y. Urbach

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我们将d维时空中自由或临界O(N)(或U(N))玻色矢量模型的路径积分明确地重写为(d + 1)维反德西特空间上的场(包括无质量高自旋场)上的路径积分。受de Mello Koch、Jevicki、Suzuki和Yoon等人的启发,我们首先用双局域场重写矢量模型,然后将这些场展开到共形群的本征模中,最后将这些本征模映射到反de Sitter空间上的场.我们的结果提供了一个明确的(非本地)反德西特空间的高自旋理论的行动,这大概是等价的大N限制瓦西里耶夫的经典高自旋引力理论(与一些特定的规范固定到一个固定的背景),但它也可以用于循环计算。我们的映射是明确的1/N扩展内,但原则上也可以扩展到有限N理论,其中需要考虑散装领域的产品的额外限制。
We explicitly rewrite the path integral for the free or critical O(N) (or U(N)) bosonic vector models in d space-time dimensions as a path integral over fields (including massless high-spin fields) living on (d + 1)-dimensional anti-de Sitter space. Inspired by de Mello Koch, Jevicki, Suzuki and Yoon and earlier work, we first rewrite the vector models in terms of bi-local fields, then expand these fields in eigenmodes of the conformal group, and finally map these eigenmodes to those of fields on anti-de Sitter space. Our results provide an explicit (non-local) action for a high-spin theory on anti-de Sitter space, which is presumably equivalent in the large N limit to Vasiliev’s classical high-spin gravity theory (with some specific gauge-fixing to a fixed background), but which can be used also for loop computations. Our mapping is explicit within the 1/N expansion, but in principle can be extended also to finite N theories, where extra constraints on products of bulk fields need to be taken into account.
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