发表机构
Instituto de Física Teórica, UNESP-Universidade Estadual Paulista（圣保罗州立大学理论物理研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究利用全息宇宙学三维玩具模型，通过全息字典和对偶性，将应力 - 能量张量三点函数与度量和磁单极场交叉相关性联系，计算相关项及非线性参数，发现标量 - 单极交叉相关性主导阶消失，张量 - 单极交叉相关性非零，为全息宇宙学实验测试指出新方向。
AI 中文摘要
在本文中，我们使用全息宇宙学的三维玩具模型，给出了应力 - 能量张量的三点函数$\langle TJJ \rangle$以及两个$SO(3)$全局流插入的一圈计算。通过应用将这些量子场论$n$点函数与宇宙学关联函数联系起来的全息字典，以及将电诺特流映射到与宇宙学磁单极对偶的磁涡旋流的$Sl(2,\mathbb{Z})$对偶性，我们将$\langle TJJ \rangle$关联函数与度量扰动和体磁单极场之间的交叉相关性联系起来，具体映射到非高斯性$\langle \xi \tilde{A} \tilde{A} \rangle$和$\langle \gamma \tilde{A} \tilde{A} \rangle$。我们计算了在挤压极限$p_1 \to 0$下实现宇宙学关联函数精确因式分解所需的半局部接触项。最后，我们评估了有效的非线性参数，表明标量 - 单极交叉相关性在主导阶消失，$f_{NL}^{\xi \tilde{A} \tilde{A}} = 0$，而张量 - 单极交叉相关性产生非零的$f_{NL}^{\gamma\tilde A\tilde A}$。这些结果符合非高斯关联函数预期的幅度层次，同时指出了全息宇宙学可通过实验测试的新方向。
英文摘要
In this paper, we present the 1-loop calculation of the three-point function $\langle TJJ \rangle$ of the stress-energy tensor and two insertions of $SO(3)$ global currents, using a 3d toy model for holographic cosmology. By applying the holographic dictionary that relates these QFT $n$-point functions to cosmological correlators, together with the $Sl(2,\mathbb{Z})$ duality that maps the electric Noether current to a magnetic vortex current dual to cosmological magnetic monopoles, we relate the $\langle TJJ \rangle$ correlator to the cross-correlations between metric perturbations and the bulk magnetic monopole field, specifically mapping to the non-Gaussianities $\langle ξ\tilde{A} \tilde{A} \rangle$ and $\langle γ\tilde{A} \tilde{A} \rangle$. We calculate the semi-local contact terms necessary to achieve the exact factorization of the cosmological correlators in the squeezed limit, $p_1 \to 0$. Finally, we evaluate the effective non-linear parameters, showing that the scalar-monopole cross-correlation vanishes at leading order, $f_{NL}^{ξ\tilde{A} \tilde{A}} = 0$, while the tensor-monopole cross-correlation yields a non-zero $f_{NL}^{γ\tilde A\tilde A}$. These results respect the expected amplitude hierarchy of the non-Gaussian correlators, while pointing at new directions in which holographic cosmology can be tested experimentally.
Comments45 pages, 1 figure; appendix and clarifying remarks added, reference added
