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 not
know 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 correspondence
in 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 the
consideration 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.