Agujeros Needles con Pelo y Dualidad AdS/CFT
Agujeros Negros con Pelo y Dualidad AdS/CFT
摘要：
本论文基于先前发表在[arXiv：1501.04252，arXiv：1511.08759，arXiv：1606.07870]中的材料，并按以下方式组织。第二章证明了时空AdS的等距群与对偶CFT理论的共形群是完全（同构）匹配的。给出了AdS/CFT对偶的精确公式，描述了AdS时空中大质量标量场的行为.在第三章中，我们给出了在文献中广为人知的黑洞解，我们将在后面的计算中使用这些解来获得直观，我们解释了无毛定理和两个可以避开这个定理的精确黑洞解的例子。这些结果发表在[arXiv：1211.2765，arXiv：1311.6065，arXiv：1311.7459]中。第四章详细介绍了全息重整化方法和哈密顿方法，这些方法在后面的章节中得到了应用。对于SAdS的求解，计算了壳层作用量并进行了正则化，与背景扣除法进行了比较。第5章是基于[arXiv：1606.07870]。本文研究了标量场与引力最小耦合且具有共形质量$m^{2}=-2/l^{2}$的AdS的边界条件，分别为非对数分支和对数分支。我们计算了在壳作用量，研究了变分原理，并提出了新的反作用项。第六章，在[arXiv：1501.04252，arXiv：1606.07870]的基础上，我们描述了具有标量头发和视界平坦和球形的黑洞的相变。我们建立了热力学相图，并讨论了它们在对偶量子场论中的应用。最后在第七章中给出了本文的结论和未来的工作方向。
英文摘要：
The present thesis is based in the material previously published in [arXiv:1501.04252, arXiv:1511.08759, arXiv:1606.07870] and it is organized in the following way. The second chapter is shown as the isometric group of the space time AdS is exactly (isomorphic) match to the conformal group of the dual CFT theory. We present the precise formulation of the duality AdS/CFT and we describe the behavior of a massive scalar field in AdS space-time. In chapter 3 we present solutions of black holes widely known in the literature, which we will use in some later calculations to gain intuition, we explain the no-hair theorem and two examples of exact black hole solutions that can evade this theorem. These results were published in [arXiv:1211.2765, arXiv:1311.6065, arXiv:1311.7459]. Chapter 4 we present details of the methods of holographic renormalization and Hamiltonian formalism, which are applied in the development of the later chapters. For the solution SAdS calculate the on-shell action and regularize, compare with the method of subtraction of the background. Chapter 5 is based on [arXiv:1606.07870]. We investigated the boundary conditions of AdS in the presence of a scalar field minimally coupled to gravity with conformal mass $m^{2}=-2/l^{2}$, for non-logarithmic and logarithmic branch. We calculate the on-shell action, we study the variational principle and propose new counter-terms that regularize the action. Chapter 6, is based on [arXiv:1501.04252, arXiv:1606.07870], we describe the phase transitions of black holes with scalar hair and horizons flat and spherical. We build the thermodynamic phase diagrams and discuss their implications in the dual quantum field theory. Finally in chapter 7 the conclusions and future directions of the work are presented.
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