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arXiv 1607.07077hep-th
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五维临界O（N）模型中的自举混合关联函数

Bootstrapping Mixed Correlators in the Five Dimensional Critical O(N) Models

Zhijin Li, Ning Su

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28 pages, 4 figures
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摘要：

我们使用共形引导方法来探索具有$O(N)$全局对称性的$5D$ CFTs，其中包含$N$标量$ϕ_i$变换为$O(N)$向量。具体而言，我们研究了领先的$O(N)$载体$ϕ_i$和$O(N)$单线态$σ$的多个四点关联函数。四点函数的交叉对称性和么正性条件对$ϕ_i$和$σ$的标度维数（$Δ_ϕ$，$Δ_σ$）提供了非平凡的约束。通过对$ϕ_i$（$σ$）和下一个$O(N)$向量（单线态）标量的缩放维度之间的间隙的合理假设，我们能够隔离小岛中的缩放维度$(Δ_ϕ$、$Δ_σ)$。特别地，对于大的$N=500$，孤立区域与从大的$N$展开获得的结果高度一致。我们还研究了$1\leqslant N\leqslant100$的相互作用$O(N)$ CFTs。$(Δ_ϕ,Δ_σ)$平面上的孤立区域使用保角引导程序与低阶导数$Λ$得到，但是，它们消失后，增加$Λ$。我们认为这些岛对应于相互作用但非单一的$O(N)$ CFTs。我们的结果提供了一个下限的临界值$N_c>100$，低于该相互作用的$O(N)$ CFTs变成非幺正。与以前的估计相比，临界值出乎意料地大。

英文摘要：

We use the conformal bootstrap approach to explore $5D$ CFTs with $O(N)$ global symmetry, which contain $N$ scalars $ϕ_i$ transforming as $O(N)$ vector. Specifically, we study multiple four-point correlators of the leading $O(N)$ vector $ϕ_i$ and the $O(N)$ singlet $σ$. The crossing symmetry of the four-point functions and the unitarity condition provide nontrivial constraints on the scaling dimensions ($Δ_ϕ$, $Δ_σ$) of $ϕ_i$ and $σ$. With reasonable assumptions on the gaps between scaling dimensions of $ϕ_i$ ($σ$) and the next $O(N)$ vector (singlet) scalar, we are able to isolate the scaling dimensions $(Δ_ϕ$, $Δ_σ)$ in small islands. In particular, for large $N=500$, the isolated region is highly consistent with the result obtained from large $N$ expansion. We also study the interacting $O(N)$ CFTs for $1\leqslant N\leqslant100$. Isolated regions on $(Δ_ϕ,Δ_σ)$ plane are obtained using conformal bootstrap program with lower order of derivatives $Λ$; however, they disappear after increasing $Λ$. We think these islands are corresponding to interacting but nonunitary $O(N)$ CFTs. Our results provide a lower bound on the critical value $N_c>100$, below which the interacting $O(N)$ CFTs turn into nonunitary. The critical value is unexpectedly large comparing with previous estimations.

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