论文标题
矢量模型的AD/CFT的推导
A Derivation of AdS/CFT for Vector Models
论文作者
论文摘要
我们明确地重写了免费或关键$ O（n）$（或$ u（n）$）的bosonic矢量模型的路径积分，以$ d $时空尺寸为居住在（$ d+1 $）的田野（包括无数的高速自动磁场）的路径积分中。受到德梅洛·科赫（De Mello Koch），杰维奇（Jevicki），铃木（Suzuki）和尹（Yoon）以及早期工作的启发，我们首先根据双本地领域重写了矢量模型，然后在保形组的特征元中扩展了这些领域，最后将这些特征模型映射到抗Anti-de satter satter上的田野。我们的结果为抗DE保健空间的高自旋理论提供了明确的（非本地）作用，该理论大概是在大的$ n $限制中与Vasiliev的经典高旋转重力理论（具有固定背景的某些特定的量规）相等，但也可以用于循环计算。我们的映射在$ 1/n $扩展中明确，但原则上也可以扩展到有限的$ n $理论，其中需要考虑对散装领域产品的额外约束。
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.
