论文标题
有限$ n $，体积和温度的矢量模型的显式全息图
Explicit holography for vector models at finite $N$, volume and temperature
论文作者
论文摘要
在以前的工作中，我们在$ d $ dimensions中的大型$ n $ vector模型（免费或关键）之间构建了一个明确的映射，以及$ ads_ {d+1} $的非本地高旋转重力理论，使得引力理论以$ 1/n $ $ 1/n $中的顺序重现了现场理论相关函数。在本文中，我们讨论了该映射的三个方面。首先，我们的原始映射在$ 1/n $中无效，因为它不包含出现在有限$ n $的重力场之间的非本地相关性。我们表明，通过使用类似于SYK模型中使用的BI-LELEAMAL $ G-σ$类型形式主义，我们可以构建一个精确的映射到散装的批次，该映射在有限的$ n $中也有效。批量中的理论包含实施有限$ n $约束的其他辅助领域。其次，我们讨论了对$ s^d $的映射到现场理论的概括，尤其是球体自由能如何在双方之间恰好匹配，以及如何始终如一地进行映射。最后，我们在有限温度下讨论了场理论，并表明矢量模型的低温相可以映射到热广告空间上的高旋转重力理论。
In previous work we constructed an explicit mapping between large $N$ vector models (free or critical) in $d$ dimensions and a non-local high-spin gravity theory on $AdS_{d+1}$, such that the gravitational theory reproduces the field theory correlation functions order by order in $1/N$. In this paper we discuss three aspects of this mapping. First, our original mapping was not valid non-perturbatively in $1/N$, since it did not include non-local correlations between the gravity fields which appear at finite $N$. We show that by using a bi-local $G-Σ$ type formalism similar to the one used in the SYK model, we can construct an exact mapping to the bulk that is valid also at finite $N$. The theory in the bulk contains additional auxiliary fields which implement the finite $N$ constraints. Second, we discuss the generalization of our mapping to the field theory on $S^d$, and in particular how the sphere free energy matches exactly between the two sides, and how the mapping can be consistently regularized. Finally, we discuss the field theory at finite temperature, and show that the low-temperature phase of the vector models can be mapped to a high-spin gravity theory on thermal AdS space.
