dS中的高自旋关联函数
Higher-Spin Correlators in dS
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中文总结 AI 辅助
本研究借助全息矢量模型描述，分析dS₄中最小高自旋引力的动量空间关联函数，推导无虚假奇点的五点函数表示，验证其共形不变性并提出高自旋关联函数的组合bootstrap思路。
中文摘要 AI 辅助
我们利用最小高自旋引力在dS₄中的全息矢量模型描述，研究其动量空间关联函数。该模型中的连通n点函数由三维单圈积分表示，是边界运动学的有理函数。我们证明四点函数具有非平凡几何特征：其物理奇点由对偶动量四边形的托勒密关系支配。在五点时，五边形积分引入表观主导朗道奇点，我们证明该奇点是虚假的，施加格拉姆约束后会消失。我们推导了无虚假奇点、以图论基本模块组织的五点函数表示，随后验证了这些关联函数的共形不变性，并讨论其在软极限、坍缩极限和托勒密极限下的行为。该结构暗示了一般多重度高自旋关联函数的组合bootstrap方法，其中共形不变性和物理奇点源自底层图组合学。
英文摘要
We study momentum-space correlators in minimal higher-spin gravity in $\mathrm{dS}_4$ using its holographic vector-model description. Connected $n$-point functions in this model are represented by three-dimensional one-loop integrals and are rational functions of the boundary kinematics. We show that the four-point function displays a nontrivial geometric feature: its physical singularity is governed by a Ptolemy relation for the dual momentum quadrilateral. At five points, the pentagon integral introduces an apparent leading Landau singularity, which we show is spurious and disappears once the Gram constraint is imposed. We derive a representation of the five-point function free of spurious singularities and organized in terms of graph-theoretic building blocks. We then verify the conformal invariance of these correlators and discuss their behavior in the soft, collapsed, and Ptolemy limits. This structure suggests a combinatorial bootstrap for higher-spin correlators at general multiplicity, in which conformal invariance and the physical singularities emerge from the underlying graph combinatorics.
