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arXiv 2305.15664hep-thgr-qc
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AdS 时空中的宇宙弦和膜诱导的真空极化

Vacuum polarization induced by a cosmic string and a brane in AdS spacetime

W. Oliveira dos Santos, E. R. Bezerra de Mello

AI总结:

本文在 braneworld 模型中研究了携带磁通量的宇宙弦与膜在 $(D+1)$ 维 AdS 时空下对带电标量场诱导的真空极化,构造 Wightman 函数计算了场平方和能量-动量张量的真空期望值,并分析了膜与弦诱导效应的相对贡献及渐近行为。

摘要:

本文在 braneworld 模型背景下,研究了由携带磁通量的宇宙弦在 $(D+1)$ 维 anti-de Sitter 背景上对带电量子大质量标量场诱导的真空极化效应。我们考虑膜平行于 anti-de Sitter 边界,且宇宙弦与它们正交。此外,假设场在膜上满足 Robin 边界条件。由于膜将空间划分为两个具有不同量子真空性质的区域,我们分别计算了各区域中场平方的真空期望值(VEV)和能量-动量张量(EMT)。为开展这些分析,我们为两个区域构造了正频 Wightman 函数。后者被分解为仅存在宇宙弦的 anti-de Sitter bulk 关联部分,以及由膜诱导的另一部分。文献已研究高维 anti-de Sitter bulk 中存在宇宙弦时的真空极化效应,因此本文主要关注由膜诱导的效应。我们证明,宇宙弦诱导的场平方 VEV 和 EMT 分量在膜上是有限的。具体而言,我们将这些可观测量与仅由膜诱导的对应量进行比较,结果表明:在靠近膜处,膜诱导的贡献大于弦诱导的贡献;然而,在远离膜的区域,情况发生逆转。此外,还针对模型物理参数的特定极限情况,提供了场平方 VEV 和 EMT 的渐近表达式。最后,将结果应用于具有单膜的 $Z_2$ 对称 Randall-Sundrum braneworld 模型中的宇宙弦情形。

英文摘要:

In this paper we investigate the vacuum polarization effects associated to a charged quantum massive scalar field on a $(D+1)$-dimensional anti-de Sitter background induced by a magnetic-flux-carrying cosmic string in the braneworld model context. We consider the brane parallel to the anti-de Sitter boundary and the cosmic string orthogonal to them. Moreover, we assume that the field obeys the Robin boundary condition on the brane. Because the brane divides the space into two regions with different properties of the quantum vacuum, we calculate the vacuum expectation value (VEV) of the field squared and the energy-momentum tensor (EMT) in each region. To develop these analyses, we have constructed the positive frequency Wightman function for both regions. The latter is decomposed in a part associated with the anti-de Sitter bulk in the presence of a cosmic string only, and the other part induced by the brane. The vacuum polarization effects associated with the higher-dimensional anti-de Sitter bulk in the presence of cosmic string have been developed in the literature, and here we are mainly interested in the effects induced by the brane. We show that the VEVs of the field squared and the components of the EMT induced by the cosmic string are finite on the brane. Explicitly, we compare these observables with the corresponding ones induced by the brane only, and show that near the brane the contribution induced by the latter is larger than the one induced by the string; however, for points distant from the brane the situation is reversed. Moreover, some asymptotic expressions for the VEV of the field squared and EMT are provided for specific limiting cases of the physical parameters of the model. Also, an application of our results is given for a cosmic string in the $Z_2$-symmetric Randall-Sundrum braneworld model with a single brane.

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