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arXiv 1401.7016hep-th
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偶维AdS配分函数的拟正规模方法

Partition Functions in Even Dimensional AdS via Quasinormal Mode Methods

Cynthia Keeler, Gim Seng Ng

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27 pages; v2: minor updates and JHEP version
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摘要：

本文利用Denef，Hartnoll和Sachdev在arXiv：0908.2657中提出的拟正规模方法，计算了偶数维AdS $_{d+1}$空间中质量标量（具有共形维数$Δ$）的单圈行列式.工作首先在二维相关的欧几里德双曲平面$H_2$，我们发现一系列的零模式的负实值的$Δ$的存在表明一系列的极点在一个循环的配分函数$Z(Δ)$在$Δ$复平面，这些极点贡献温度无关的条款计算arXiv：0908.2657热AdS配分函数。我们的结果与Camporesi和Higuchi的一系列论文以及Gopakumar等人在arXiv：1103.3627和Banerjee等人在arXiv：1005.3044中的结果相匹配。我们还研究了这些零模式的意义，发现它们威克旋转的AdS $_2$黑洞的准正常模式。它们也可解释为$S^1$上光滑函数空间中$SO(2,1)$的离散级数表示的矩阵元素。我们将我们的结果推广到一般偶数维AdS $_{2n}$，再次找到一系列的零模式，这是相关的离散系列表示的$SO(2n,1)$，运动组的$H_{2n}$。

英文摘要：

In this note, we calculate the one-loop determinant for a massive scalar (with conformal dimension $Δ$) in even-dimensional AdS$_{d+1}$ space, using the quasinormal mode method developed in arXiv:0908.2657 by Denef, Hartnoll, and Sachdev. Working first in two dimensions on the related Euclidean hyperbolic plane $H_2$, we find a series of zero modes for negative real values of $Δ$ whose presence indicates a series of poles in the one-loop partition function $Z(Δ)$ in the $Δ$ complex plane; these poles contribute temperature-independent terms to the thermal AdS partition function computed in arXiv:0908.2657. Our results match those in a series of papers by Camporesi and Higuchi, as well as Gopakumar et al. in arXiv:1103.3627 and Banerjee et al. in arXiv:1005.3044. We additionally examine the meaning of these zero modes, finding that they Wick-rotate to quasinormal modes of the AdS$_2$ black hole. They are also interpretable as matrix elements of the discrete series representations of $SO(2,1)$ in the space of smooth functions on $S^1$. We generalize our results to general even dimensional AdS$_{2n}$, again finding a series of zero modes which are related to discrete series representations of $SO(2n,1)$, the motion group of $H_{2n}$.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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