Holography of accelerating black holes

加速黑洞的全息术

• 批准号: 2426436
• 金额: --
• 依托单位: University of Oxford
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2020
• 资助国家: 英国
• 起止时间: 2020 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2426436
• 关键词: Holography; accelerating; black; holes

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.

本计画福尔斯属于EPSRC的“数学物理”与“几何与拓扑学”研究领域。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机制可以被用作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对象，但它们的一些基本方面今天仍然知之甚少，特别是那些与它们的物理行为有关的方面（例如微观描述，信息悖论）。最近受到极大关注的一类黑洞是渐近AdS黑洞。虽然据我们所知，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进行研究：全息原理。根据这个想法，人们可以尝试提供一个微观描述的统计自由度的基础上的黑洞热力学的CFT生活在边界上的AdS，这是对偶的黑洞解决方案。这一策略已经成功地应用于各种各样的情况，但还有许多其他的情况仍有待研究。该项目的目的是构建新的低维超引力黑洞的一般类别，并试图从全弦理论的角度更系统地理解它们的微观描述。我们将首先考虑一个具有渐近AdS_4几何和五个不同参数的四维黑洞族：质量、电荷和磁荷、角动量和加速度。尽管爱因斯坦-麦克斯韦理论的这个解很早以前就被人们所知，但到目前为止还没有得到太多的研究。我们的工作的出发点是正确地确定它的边界几何，然后通过全息计算再现这种黑洞的Bekenstein-Hawking熵，我们将在文献中研究的通常带电和旋转的AdS_4黑洞中加入一个主要的新成分，即非零加速度的存在。值得注意的是，这相当于考虑一个显示圆锥奇点的度量，因此与加权射影空间相一致。由于与全息对偶场理论相关的技术原因，我们将专注于BPS黑洞，即超对称和极端的黑洞。这些要求对自由参数施加了约束，将独立参数的数量从五个减少到两个。另一方面，在零温度下，近视界几何本质上是一个无限的喉道，连接黑洞熵与重整化壳作用量的量子统计关系是先验无效的。在这些情况下的标准程序预见了一个正则化的问题，通过分析延续的一些参数的复平面，其次是采取BPS限制沿着一个超对称的轨迹在参数空间。通过这个过程，应该可以恢复一种在零温度下也有效的量子统计关系。我们的策略将是应用这个BPS限制程序，并确定边界几何，这是如何进入黑洞的解决方案的参数影响的渐近几何。有了这个结果，我们将考虑一个生活在这样一个边界上的SCFT，并试图通过精确计算配分函数来重现黑洞的贝肯斯坦-霍金熵。最近，人们在系统地研究弯曲空间上的超对称理论上投入了大量的精力，我们的工作将恰好落在这个框架中。