Bootstrapping Holography

自举全息术

• 批准号: 2567207
• 金额: --
• 依托单位: Durham University
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2021
• 资助国家: 英国
• 起止时间: 2021 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2567207
• 关键词: Bootstrapping; Holography

Demanding only the minimal criteria of symmetries and mathematical-consistency, the Bootstrap approach to scattering theory has given rise to a variety of different ways to con-strain and extract predictions from physical theories. Requiring only self-consistency as an input, approaches like the Bootstrap are becoming increasingly relevant in efforts to address the shortcomings in our understanding of our Universe at energies where we currently have little guidance from experiment, such as in its earliest moments and the related search for a complete quantum theory of gravity. The consistency criteria that should be satisfied by scattering amplitudes are however still to be fully determined in other words, we currently do notknow all the rules of the game that we are playing! Recent years have seen significant progress in this direction with the emergence of new physical insights, in particular the striking notion that Quantum Gravity is "holographic" in nature in studying Quantum Gravity, we are led to consider holographic theories for the boundary observable infinity. This has provided us with a spectacular working example of a scenario in which we know very well the rules of the game: The AdS/CFT correspondence, where boundary observables of Quantum Gravity in asymptotically anti-de Sitter(AdS) space can be recast as correlation functions of a Conformal Field Theory(CFT).The latter are completely specified by a combination of conformal symmetry, unitarity and associativity of the operator algebra, which are used to carve out the space of consistent CFTs (and hence quantum gravities in AdS space) within the so-called Conformal Bootstrap programme. This, in turn, has given rise to a variety of powerful techniques to study scattering in AdS space.Given this, in the research project the student will explore the following question:Can we extend the Bootstrap of observables on the boundary of anti-de Sitterspace to encompass scenarios closer to that of our own Universe?The focus will be on in de Sitter (dS) space (and potentially also at space), whose boundary, in contrast to that of AdS, is space-like and hence lacks a standard notion of locality and time. The set-up is therefore a step away from the relative security of the AdS/CFT correspondencein a direction where we might learn something fundamentally new about holography itself the emergence of time. In other words, how might consistent time evolution be encoded mathematically in spatial correlations on the boundary of dS space? At the same time theconsideration of dS space retains some familiar features of the AdS/CFT set-up, including conformal symmetry of the observables, which might be used as scaffolding to import techniques and intuition from AdS to dS.The student project will build upon recent work [1, 2, 3, 4, 5] of the supervisor in this direction, which developed a formalism that places boundary correlators in AdS and dS on the same footing. Within this framework one can straightforwardly derive relations between the boundary correlators in the two space-times, which allow to directly import techniques and results from AdS to dS. This will serve as a starting point for the project, where the student will explore what we can learn about the structure of dS correlators using such relations and, moreover, by importing existing successful techniques for studying scattering in AdS space, use them to derive new results for dS correlators of phenomenological interest which thus far have been intractable.

只需要对称性和数学一致性的最低标准，散射理论的Bootstrap方法已经产生了各种不同的方法来约束和提取物理理论的预测。只需要自我一致性作为输入，像Bootstrap这样的方法在努力解决我们对宇宙理解中的缺陷的努力中变得越来越重要，这些能量目前我们几乎没有从实验中获得指导，比如在宇宙的最早时刻，以及相关的对完整的引力量子理论的探索。然而，散射幅度应该满足的一致性标准仍然有待完全确定，换句话说，我们目前并不知道我们正在玩的游戏的所有规则！近年来，随着新的物理观点的出现，特别是量子引力在本质上是“全息”的这一引人注目的概念的出现，我们在这个方向上取得了重大进展。在研究量子引力时，我们被引导去考虑边界可见无穷大的全息理论。这为我们提供了一个壮观的工作例子，其中我们非常了解游戏规则：ADS/CFT对应，其中渐近反德西特(ADS)空间中量子引力的边界可观测值可以被重塑为共形场论(CFT)的关联函数。CFT完全由算符代数的共形对称性、酉性和结合性的组合来描述，这些算符代数被用来在所谓的共形Bootstrap程序中划分出相容的CFT空间(从而在ADS空间中的量子引力)。这反过来又产生了研究ADS空间散射的各种强大的技术。鉴于此，在研究项目中，学生将探索以下问题：我们能否扩展反de Sitterspace边界上的可观测的Bootstrap，以涵盖更接近我们自己宇宙的场景？重点将放在De Sitter(DS)空间(可能也在空间)，与ADS的边界相反，其边界类似于空间，因此缺乏位置和时间的标准概念。因此，这一设置远离了ADS/CFT通信的相对安全性，朝着一个我们可能会从根本上了解全息术本身的新东西--时间的出现--的方向前进了一步。换句话说，一致的时间演化如何在数学上编码为DS空间边界上的空间相关性？同时，DS空间的考虑保留了ADS/CFT设置的一些熟悉的特征，包括可观测的共形对称性，这可以被用作将技术和直觉从ADS引入DS的脚手架。学生项目将建立在主管在这个方向上的最新工作[1，2，3，4，5]的基础上，该工作发展了一种形式主义，将边界相关器放在ADS和DS中处于相同的基础上。在这个框架内，人们可以直接推导出两个时空中边界相关器之间的关系，从而允许直接将ADS中的技术和结果引入DS。这将作为项目的起点，在这里，学生将探索我们可以使用这种关系从DS相关器的结构中了解到什么，而且，通过引入现有的研究广告空间中散射的成功技术，使用它们来为具有现象学意义的DS相关器得出到目前为止难以解决的新结果。