Repository logo

On the Relationship between Canonical Quantum Gravity and the Holographic Principle



Change log


Araujo Regado, Goncalo 


This thesis explores the connection between two approaches to the problem of quantum gravity. On the one hand, we have the canonical approach which imposes the gauge constraints on the physical states. This leads to the notoriously hard problem of solving the Wheeler-deWitt (WdW) equation. On the other hand, we have the holographic principle, which defines the gravitational path integral in terms of the partition function of a non-gravitational CFT living on the boundary, leading to the flourishing field of the AdS/CFT correspondence. The connection between the two becomes clear after a reformulation of the holographic principle in which the emergent dimension is time instead of space. For that we need to consider Euclidean field theories living on a slice of space. They are defined starting from the usual type of holographic CFTs followed by a special type of deformation called the T2 deformation. Such partition functions solve the WdW equation, thus providing canonical quantum states of the bulk theory. The deformation flow is uniquely fixed by the bulk gauge constraints and it has several exotic properties. This formulation extends the AdS/CFT framework naturally to other quantum gravity scenarios.

We explain the what, how and why of the T2 deformation in quantum gravity by studying general solutions to the WdW equation. This leads naturally to an explicit map between field theory states living on the boundary of space and quantum gravity states living on the bulk of space. This is a manifestation of the holographic principle, hiding inside the WdW equation. We also propose a reconstruction of the boundary state from bulk data. We conjecture about an isomorphism between the quantum gravity and field theory Hilbert spaces. The dynamics of the boundary state with respect to boundary time is shown to induce a time evolution of the quantum gravity state. We discuss, at several points in the thesis, how the bulk theory manages to keep being unitary, despite the lack of unitarity of the deformed field theory. Along the way, we also propose a more general version of the holographic principle in the language of equating bulk and boundary path integrals.

We discuss at length the application of this formalism to quantum cosmology. This requires us to consider complexified deformations. Crucially, we are forced to consider superpositions of field theory branches in order to describe the bulk. This leads to several discussions about the structure of quantum gravity and its hypothetical UV completion. In particular, we discuss the phenomenon of spontaneous CPT breaking for the UV completion of the T2-deformed theory along its RG flow. The partition function is computed explicitly in minisuperspace, touching base with previously known solutions to the WdW equation applied to this restricted toy model. We then go on to conjecture that the choice of lapse contour in the gravitational path integral is intimately related to the superposition of field theory branches and, therefore, to the different UV completions for the holographic dual. All these features point in the direction of the long-standing conjecture that there is a unique quantum state of the universe.





Wall, Aron


holography, quantum cosmology, quantum gravity


Doctor of Philosophy (PhD)

Awarding Institution

University of Cambridge