Holography of accelerating black holes

该项目属于EPSRC的“数学物理”和“几何与拓扑”研究领域。高能理论物理学中一个广泛的研究领域与黑洞有关。这些物体构成了一个特别有趣的工作领域，因为它们产生的极端引力状态可以作为研究量子引力某些特征的游乐场。此外，尽管它们是相当简单的物体，但它们的一些基本方面至今仍知之甚少，特别是与它们的热力学行为有关的方面（例如微观描述、信息悖论）。最近，一类特殊的黑洞受到了极大的关注，那就是渐近AdS黑洞。尽管据我们所知，它们与现实没有明确的联系，但它们很有趣，因为它们允许通过一个非常强大的工具来研究：全息原理。按照这个想法，人们可以尝试提供一个微观的描述，根据生活在黑洞解对偶的AdS边界上的CFT来描述黑洞热力学的统计自由度。这一策略确实在各种各样的案例中得到了成功的应用，但仍有许多其他案例有待研究。该项目的目的是在低维超重力下构建新的一般黑洞类别，并试图从全弦理论的角度更系统地理解它们的微观描述。有了这个广阔的图景，我们将从考虑一个四维黑洞家族开始，它们具有渐近的AdS_4几何形状和五个不同的参数：质量、电荷和磁荷、角动量和加速度。尽管人们很早以前就知道爱因斯坦-麦克斯韦理论的这个解，但直到今天人们还没有对它进行过多的研究。我们项目的出发点将是正确识别它的边界几何形状，然后通过全息计算再现这样一个黑洞的贝肯斯坦-霍金熵。我们将在文献中研究的通常带电和旋转的AdS_4黑洞中添加的主要新成分是存在不消失的加速度。值得注意的是，这相当于考虑一个度量，它显示圆锥奇点，因此与加权射影空间一致。由于与全息对偶场论相关的技术原因，我们将重点关注BPS黑洞，即超对称和极值的黑洞。这些要求对自由参数施加了约束，将独立参数的数量从5个减少到2个。另一方面，在零温度下，近视界几何本质上是一个无限的咽喉，连接黑洞熵与重归一化壳层作用的量子统计关系先验地无效。在这些情况下，标准程序通过将一些参数解析延拓到复平面，然后在参数空间中沿超对称轨迹取BPS极限，来预测问题的正则化。通过这个过程，应该有可能恢复在零温度下也有效的量子统计关系的形式。我们的策略将是应用这种BPS限制程序并确定边界几何，即进入黑洞解的参数如何影响渐近几何。有了这个结果，我们将考虑一个存在于这样一个边界上的SCFT，并尝试通过对配分函数的精确计算来重现黑洞的贝肯斯坦-霍金熵。最近，人们对弯曲空间的超对称理论进行了大量的系统研究，我们的工作将正好落在这个框架中。

This project falls within EPSRC "mathematical physics" and "geometry and topology" research areas.A wide area of interest within high energy theoretical physics is concerned with the study of black holes. These objects constitute a particularly interesting field of work because the extreme gravitational regimes they give rise to can be exploited as a playground for studying some of the features of quantum gravity. Moreover, despite being rather simple objects, some of their fundamental aspects are little understood still today, particularly those relative to their thermodynamical behaviour (e.g. microscopic description, information paradox). One particular class of black holes that has received a remarkable attention lately is that of asymptotically AdS black holes. Though they do not have an explicit connection to reality as far as we know, they are interesting because they allow to be studied through a very powerful tool: the holographic principle. Following this idea, one can attempt to provide a microscopic description of the statistical degrees of freedom underlying the black hole thermodynamics in terms of the CFT living on the boundary of AdS which is dual to the black hole solution. This strategy has indeed been applied with success in a wide variety of cases, yet many others are still to be studied.The aim of the project is to construct new general classes of black holes in low dimensional supergravity and try to understand more systematically their microscopic description from the full string theory perspective.With this wide picture in mind, we will start by considering a family of black holes in four dimensions with asymptotic AdS_4 geometry and five different parameters: mass, electric and magnetic charges, angular momentum, and acceleration. Despite being known since long ago, this solution of the Einstein-Maxwell theory has not been studied much up to nowadays. The starting point of our project will be to correctly identify its boundary geometry and then reproduce the Bekenstein-Hawking entropy of such a black hole through a holographic computation.The main new ingredient we will add to the usual charged and rotating AdS_4 black holes studied in literature is the presence of a non-vanishing acceleration. Remarkably, this amounts to considering a metric which displays conical singularities and therefore identifies with a weighted projective space. Due to technical reasons related to the holographically dual field theory, we will focus on BPS black holes i.e. black holes that are both supersymmetric and extremal. These requirements impose constraints on the free parameters, reducing the number of independent ones from five down to two. On the other hand, at zero temperature the near horizon geometry is essentially an infinite throat and the quantum statistical relation that connects the entropy of the black hole with the renormalised on-shell action is not valid a priori. The standard procedure in these cases foresees a regularisation of the problem by means of analytical continuation of some of the parameters to the complex plane, followed by taking the BPS limit along a supersymmetric trajectory in the parameter space. Through this procedure it should be possible to recover a form of the quantum statistical relation which is valid also at zero temperature. Our strategy will be to apply this BPS limiting procedure and identify the boundary geometry, that is how the parameters entering the black hole solution influence the asymptotic geometry. With this result in our hand we will then consider an SCFT living on such a boundary and try to reproduce the Bekenstein-Hawking entropy of the black hole through an exact computation of the partition function. Lately, a lot of effort was put on the systematic study of supersymmetric theories on curved spaces, and our work will land precisely in this framework.