带着橄榄球奔跑：余维2膜的体重正化
Running with Rugby Balls: Bulk Renormalization of Codimension-2 Branes
摘要：
我们计算如何一个循环的体积效应重整体积和膜有效的相互作用的几何来源的余维2膜。我们这样做，明确整合出自旋为零，半和一个粒子在6维爱因斯坦-麦克斯韦标量理论紧致到4维通量稳定的2D几何。(Our方法同样适用于紧化为D-2维的D维，尽管当D>6时，我们的显式公式不能捕获所有的发散。体相互作用的重正化是独立的边界条件假设在膜的位置，并重现标准的热核计算。任何特定膜的边界条件确实会影响体环如何重整化这个膜的有效作用量，但不会影响其他遥远膜的重整化。虽然我们明确计算我们的循环使用橄榄球几何，因为我们只遵循UV效果，我们的结果更普遍地适用于任何几何包含余维两个源与圆锥奇点。我们的研究结果有多种用途，包括计算紫外线的灵敏度的单圈真空能量所看到的观察员定位在膜上。我们将展示如何结合这些一个循环的影响，在一个令人惊讶的方式与批量反反应，以提供完整的低能量有效的宇宙学常数，并评论这种计算的相关性，提出应用的余维两个6D模型的解决方案的层次结构和宇宙学常数的问题。
英文摘要：
We compute how one-loop bulk effects renormalize both bulk and brane effective interactions for geometries sourced by codimension-two branes. We do so by explicitly integrating out spin-zero, -half and -one particles in 6-dimensional Einstein-Maxwell-Scalar theories compactified to 4 dimensions on a flux-stabilized 2D geometry. (Our methods apply equally well for D dimensions compactified to D-2 dimensions, although our explicit formulae do not capture all divergences when D>6.) The renormalization of bulk interactions are independent of the boundary conditions assumed at the brane locations, and reproduce standard heat-kernel calculations. Boundary conditions at any particular brane do affect how bulk loops renormalize this brane's effective action, but not the renormalization of other distant branes. Although we explicitly compute our loops using a rugby ball geometry, because we follow only UV effects our results apply more generally to any geometry containing codimension-two sources with conical singularities. Our results have a variety of uses, including calculating the UV sensitivity of one-loop vacuum energy seen by observers localized on the brane. We show how these one-loop effects combine in a surprising way with bulk back-reaction to give the complete low-energy effective cosmological constant, and comment on the relevance of this calculation to proposed applications of codimension-two 6D models to solutions of the hierarchy and cosmological constant problems.
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