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arXiv 1609.02889hep-th
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高维缺陷附近的真空极化和经典自action

Vacuum polarization and classical self-action near higher-dimensional defects

Yuri V. Grats, Pavel Spirin

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25 pages
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摘要：

我们分析了无质量标量场在高维时空中的引力诱导效应，该时空是$(d-n)$维Minkowski空间和具有立体/平面角度亏损的$n$维球/柱对称空间的张量积。这些时空被认为是具有$(d-n-1)$平坦额外维度的多维全局弦（如果是\mbox{$n\geqslant 3$}）或宇宙弦（如果是$n=2$）的简单模型。因此，我们称它们为圆锥形背景。在角度亏损值方面，我们推导出标量格林函数的微扰表达式，适用于任何$d\geqslant 3$和$2\leqslant n\leqslant d-1$，并计算它的领导阶。利用这个格林函数，我们计算了场平方$\langle ϕ^{2}(x)\rangle_{\mathrm{ren}}$的重整化真空期望值和标量场能量-动量张量$\langle T_{M N}(x)\rangle_{\mathrm{ren}}$的重整化真空平均值，对于任意的$d$和$n$，从上述区间和任意的耦合常数到曲率$ξ$ .特别是，我们重新计算的真空极化效应的非最小耦合无质量标量场在一个直宇宙弦的时空。同样的格林函数使得我们能够考虑一个经典的点状标量或电荷的引力诱导自作用的古老的纯经典问题，这些标量或电荷静止在所考虑的空间的某个固定点上。为了处理分歧，这两个问题的考虑出现，我们采用的维数正则化技术，广泛应用于量子场论（QFT）。的显式依赖的结果上的体积和锥形子流形的维数，进行了讨论。

英文摘要：

We analyze the gravity-induced effects associated with a massless scalar field in a higher-dimensional spacetime being the tensor product of $(d-n)$-dimensional Minkowski space and $n$-dimensional spherically/cylindrically-symmetric space with a solid/planar angle deficit. These spacetimes are considered as simple models for a multidimensional global monopole (if \mbox{$n\geqslant 3$}) or cosmic string (if $n=2$) with $(d-n-1)$ flat extra dimensions. Thus, we refer to them as conical backgrounds. In terms of the angular deficit value, we derive the perturbative expression for the scalar Green's function, valid for any $d\geqslant 3$ and $2\leqslant n\leqslant d-1$, and compute it to the leading order. With the use of this Green's function we compute the renormalized vacuum expectation value of the field square $\langle ϕ^{2}(x)\rangle_{\mathrm{ren}}$ and the renormalized vacuum averaged of the scalar-field's energy-momentum tensor $\langle T_{M N}(x)\rangle_{\mathrm{ren}}$ for arbitrary $d$ and $n$ from the interval mentioned above and arbitrary coupling constant to the curvature $ξ$. In particular, we revisit the computation of the vacuum polarization effects for a non-minimally coupled massless scalar field in the spacetime of a straight cosmic string. The same Green's function enables to consider the old purely classical problem of the gravity-induced self-action of a classical pointlike scalar or electric charge, placed at rest at some fixed point of the space under consideration. To deal with divergences, which appear in consideration of the both problems, we apply the dimensional-regularization technique, widely used in quantum field theory (QFT). The explicit dependence of the results upon the dimensionalities of both the bulk and conical submanifold, is discussed.

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