Bootstrapping Holography

散射理论的Bootstrap方法只要求对称性和物理一致性的最低标准，它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能量的理解中的缺点方面变得越来越重要，我们目前几乎没有实验指导，例如在其最早的时刻以及对完整的引力量子理论的相关研究。然而，散射振幅应该满足的一致性标准仍然有待完全确定，换句话说，我们目前还不知道我们正在玩的游戏的所有规则！近年来，随着新的物理见解的出现，在这个方向上取得了重大进展，特别是量子引力本质上是“全息”的惊人概念在研究量子引力时，我们被引导考虑边界可观察无穷大的全息理论。这为我们提供了一个壮观的工作场景，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观测量可以被重铸为共形场论（CFT）的相关函数，后者完全由算子代数的共形对称性、么正性和结合性的组合来指定，这是用来雕刻出空间的一致的CFTs（因此量子引力在AdS空间）内所谓的共形引导程序。这反过来又产生了各种强大的技术来研究AdS空间中的散射。鉴于此，在研究项目中，学生将探索以下问题：我们能否将反德西特空间边界上的可观测量的Bootstrap扩展到更接近我们自己宇宙的场景？重点将放在de Sitter（dS）空间（也可能是空间）上，与AdS相比，其边界是类空间的，因此缺乏标准的局部性和时间概念。因此，这种设置离相对安全的AdS/CFT对应关系还有一步之遥，在这个方向上，我们可能会学到一些关于全息术本身的新东西--时间的出现。换句话说，在dS空间边界上的空间相关性中，如何对一致的时间演化进行数学编码？同时，dS空间的考虑保留了AdS/CFT设置的一些熟悉的特征，包括可观测量的共形对称性，这可能被用作从AdS导入技术和直觉到dS的脚手架。学生项目将建立在导师在这个方向上的最近工作[1，2，3，4，5]的基础上，它发展了一种形式主义，将AdS和dS中的边界消除器置于相同的基础上。在这个框架内，人们可以直接推导出两个时空中的边界算子之间的关系，这允许直接将AdS的技术和结果导入dS。这将作为该项目的起点，学生将探索我们可以使用这种关系了解dS散射器的结构，此外，通过导入现有的成功技术来研究AdS空间中的散射，使用它们来获得新的结果dS散射器的现象学兴趣，迄今为止一直难以解决。

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.