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arXiv 1209.4655hep-thgr-qc
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球形黑膜相变的临界维数

On critical dimension in spherical black brane phase transition

Andrei Khmelnitsky

摘要:

研究了包裹在两球紧致化流形上的大均匀黑膜的Gregory-Laflamme不稳定性。本文推广了arXiv:hep-th/0604015的工作,其中考虑了p-环面上的紧化.球面情形的新特征是紧致化流形的非零曲率和由于内建稳定机制而不存在重标度对称性。我们计算的相变的顺序依赖于扩展的尺寸使用朗道-金兹伯格方法的数量d。发现当d > 11时,微正则系综中的均匀球形黑膜呈现出向非均匀黑膜解的稳定分支的光滑二级相变.对于微正则系综和正则系综,扩展维度的临界数量(其相变顺序发生变化)是不同的,并且与平坦复曲面紧化情况下的临界维度数量不一致。我们简要地讨论了这种不匹配的起源在不同的合奏的相变的顺序。

英文摘要:

We study the Gregory-Laflamme instability of a large uniform black brane wrapping a two-sphere compactification manifold. This paper extends the work arXiv:hep-th/0604015, where the compactifications on p-torus were considered. The new features of the spherical case are the non-zero curvature of the compactification manifold and the absence of the rescaling symmetry due to a built-in stabilization mechanism. We calculate the order of the phase transition in dependence on the number d of extended dimensions using the Landau-Ginzburg approach. It is found that for d > 11 a uniform spherical black brane in microcanonical ensemble exhibits a smooth second order phase transition towards a stable branch of non-uniform black brane solutions. The critical number of extended dimensions, for which there is a change in the order of the phase transition, is different for microcanonical and canonical ensembles and does not coincide with the critical number of dimensions in the case of the flat toric compactifications. We briefly discuss the origin of this mismatch in the orders of phase transition for the different ensembles.

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