AdS/CFT Correspondence的结构和动力学方面：严格的方法
Structural and Dynamical Aspects of the AdS/CFT Correspondence: a Rigorous Approach
摘要：
我们详细研究了由Maldacena和Witten证明的AdS/CFT对应（的一个版本），在由渐近反德西特（AAdS）时空给出的引力背景中的量子场论与在后者的共形无穷大中的共形协变量子场论之间（在彭罗斯的意义上），方面，这样：（a）是独立于（对）具体模型在量子场论，和（b）易于重铸在一个数学上严格的模具。我们采用的出发点定理证明的局部量子物理学（也称为代数量子场论）在反德西特（AdS）时空，称为代数全息或厄勒伦对偶。目前工作的主要内容是将Wehren的结果推广到一个相当一般的d维AAdS时空（d>3），仔细研究这种推广的性质与AdS时空相比是如何被削弱和/或修改的，并探索非平凡的引力效应如何在共形无穷大的量子理论中表现出来。语言雇用的量子理论有关我们的推广厄勒伦对偶遵循函式制定的局部量子物理由于Brunetti，Fredenaldi和Verch，扩大后，索默，以纳入边界条件。
英文摘要：
We elaborate a detailed study of certain aspects of (a version of) the AdS/CFT correspondence, conjectured by Maldacena and Witten, between quantum field theories in a gravitational background given by an asymptotically anti-de Sitter (AAdS) spacetime, and conformally covariant quantum field theories in the latter's conformal infinity (in the sense of Penrose), aspects such that: (a) are independent from (the pair of) specific models in Quantum Field Theory, and (b) susceptible to a recast in a mathematically rigorous mould. We adopt as a starting point the theorem demonstrated by Rehren in the context of Local Quantum Physics (also known as Algebraic Quantum Field Theory) in anti-de Sitter (AdS) spacetimes, called algebraic holography or Rehren duality. The main body of the present work consists in extending Rehren's result to a reasonably general class of d-dimensional AAdS spacetimes (d>3), scrutinizing how the properties of such an extension are weakened and/or modified as compared to AdS spacetime, and probing how non-trivial gravitational effects manifest themselves in the conformal infinity's quantum theory. The language employed for the quantum theories relevant for our generalization of Rehren duality follows the functorial formulation of Local Quantum Physics due to Brunetti, Fredenhagen and Verch, extended afterwards by Sommer in order to incorporate boundary conditions.
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