arXiv 0712.28222007-12hep-thgr-qc

经典有效场论与笼中黑洞

Classical Effective Field Theory and Caged Black Holes

Barak Kol, Michael Smolkin

备注：: 33 pages 11 figures. v2: Relatively minor changes, detailed at end of introduction
发表信息：: Phys.Rev.D77:064033,2008
DOI：: 10.1103/PhysRevD.77.064033

摘要：

匹配渐近展开是广义相对论和其他领域中的一种有用的技术，每当两个不同长度尺度的物理之间发生相互作用时。这里的匹配渐近展开被认为是相当普遍的等价于经典有效场论（CLEFT），其中一个（或多个）区域被一个有效理论所取代，该理论的术语是按照增加无关性的顺序组织的，正如戈德伯格和罗斯坦在一定的引力背景下所证明的那样。CLEFT观点的优点是过程更清晰，它允许通过费曼图表示，并且发散可以在标准场论方法中正则化和重整化。作为一个副产品，我们得到了广泛的一类经典的正则化和重整化的例子，这些概念通常与量子场论。我们通过笼中黑洞的热力学来证明这些想法，既简化了非旋转的情况，又计算了旋转的情况。特别是我们能够取代计算六个两个循环图由一个单一的可分解的两个循环图，以及计算某些新的三个循环图。结果推广到任意紧化流形。对于笼中旋转黑洞，我们得到了所有热力学量的领先修正。角动量被发现非重整化领先秩序。

英文摘要：

Matched asymptotic expansion is a useful technique in General Relativity and other fields whenever interaction takes place between physics at two different length scales. Here matched asymptotic expansion is argued to be equivalent quite generally to Classical Effective Field Theory (CLEFT) where one (or more) of the zones is replaced by an effective theory whose terms are organized in order of increasing irrelevancy, as demonstrated by Goldberger and Rothstein in a certain gravitational context. The CLEFT perspective has advantages as the procedure is clearer, it allows a representation via Feynman diagrams, and divergences can be regularized and renormalized in standard field theoretic methods. As a side product we obtain a wide class of classical examples of regularization and renormalization, concepts which are usually associated with Quantum Field Theories. We demonstrate these ideas through the thermodynamics of caged black holes, both simplifying the non-rotating case, and computing the rotating case. In particular we are able to replace the computation of six two-loop diagrams by a single factorizable two-loop diagram, as well as compute certain new three-loop diagrams. The results generalize to arbitrary compactification manifolds. For caged rotating black holes we obtain the leading correction for all thermodynamic quantities. The angular momentum is found to non-renormalize at leading order.

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