## On the Relationship between Canonical Quantum Gravity and the Holographic Principle

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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

We explain the what, how and why of the

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