半经典引力的共形不变性和表观普适性
Conformal invariance and apparent universality of semiclassical gravity
摘要：
在最近的工作中，有人指出，在静态球对称背景中，无质量标量场理论的某些观测量在大距离上表现出普适的行为。更准确地说，与曲率耦合是一般情况不同，对于特殊情况，期望值<T^μ_v>的大距离行为与引力源的内部结构无关。在这里，我们解决这个结果的高维推广：我们首先计算黑洞和静态球对称星之间的差异，在远场极限的可观测量<T^2>和<T^μ_v>。因此，我们证明了在静态球对称背景下的共形不变无质量标量场理论在D \geq 4维中具有这样的普适性现象。此外，使用单圈有效作用量，我们计算了弱引力物体的<T^μ_v>。这些结果导出了Schwarzschild-Tangherlini黑洞在远场极限下的期望值<T^μ v>的显式表达式.作为应用，我们得到了量子修正的引力势在D维，其中D=4的同意与以前发现的文献中的引力子传播子的单圈修正。
英文摘要：
In a recent work, it has been pointed out that certain observables of the massless scalar field theory in a static spherically symmetric background exhibit a universal behavior at large distances. More precisely, it was shown that, unlike what happens in the case the coupling to the curvature ξis generic, for the special cases ξ=0 and ξ= 1/6 the large distance behavior of the expectation value <T^μ_ν> turns out to be independent of the internal structure of the gravitational source. Here, we address a higher dimensional generalization of this result: We first compute the difference between a black hole and a static spherically symmetric star for the observables <ϕ^2> and <T^μ_ν> in the far field limit. Thus, we show that the conformally invariant massless scalar field theory in a static spherically symmetric background exhibits such universality phenomenon in D\geq 4 dimensions. Also, using the one-loop effective action, we compute <T^μ_ν> for a weakly gravitating object. These results lead to the explicit expression of the expectation value <T^μ_ν> for a Schwarzschild-Tangherlini black hole in the far field limit. As an application, we obtain quantum corrections to the gravitational potential in D dimensions, which for D=4 are shown to agree with the one-loop correction to the graviton propagator previously found in the literature.
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