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تسجيل مستخدم جديدNon-Perturbative 3D Quantum Gravity: Quantum Boundary States and Exact Partition Function
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We push forward the investigation of holographic dualities in 3D quantum gravity formulated as a topological quantum field theory, studying the correspondence between boundary and bulk structures. Working with the Ponzano-Regge topological state-sum model defining an exact discretization of 3d quantum gravity, we analyze how the partition function for a solid twisted torus depends on the boundary quantum state. This configuration is relevant to the AdS${}_{3}$/CFT${}_{2}$ correspondence. We introduce boundary spin network states with coherent superposition of spins on a square lattice on the boundary surface. This allows for the first exact analytical calculation of Ponzano-Regge amplitudes with extended 2D boundary (beyond the single tetrahedron). We get a regularized finite truncation of the BMS character formula obtained from the one-loop perturbative quantization of 3D gravity. This hints towards the existence of an underlying symmetry and the integrability of the theory for finite boundary at the quantum level for coherent boundary spin network states.
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We present a line of research aimed at investigating holographic dualities in the context of three dimensional quantum gravity within finite bounded regions. The bulk quantum geometrodynamics is provided by the Ponzano-Regge state-sum model, which de
fines 3d quantum gravity as a discrete topological quantum field theory (TQFT). This formulation provides an explicit and detailed definition of the quantum boundary states, which allows a rich correspondence between quantum boundary conditions and boundary theories, thereby leading to holographic dualities between 3d quantum gravity and 2d statistical models as used in condensed matter. After presenting the general framework, we focus on the concrete example of the coherent twisted torus boundary, which allows for a direct comparison with other approaches to 3d/2d holography at asymptotic infinity. We conclude with the most interesting questions to pursue in this framework.
This thesis is dedicated to the study of quasi-local boundary in quantum gravity in the 3D space-time case. This research takes root in the holographic principle, which conjectures that the geometry and the dynamic of a space-time region can be entir
ely described by a theory living on the boundary of this given region. The most studied case of this principle is the AdS/CFT correspondence, where the quantum fluctuations of an asymptotically AdS space are described by a conformal field theory living at spatial infinity, invariant under the Virasoro group. The philosophy applied in this thesis differs from the AdS/CFT case. I focus on the case of quasi-local holography, i.e. for a bounded region of space-time with a boundary at a finite distance. The objective is to clarify the bulk-boundary relation in quantum gravity described by the Ponzano-Regge model, defining a model for 3D gravity via a discrete path integral. I present the first perturbative and exact computations of the Ponzano-Regge amplitude on a torus with a 2D boundary state. After the presentation of the general framework for the 3D amplitude in terms of the 2D boundary state, I consider the 2D torus case, with application in the study of the thermodynamics of the BTZ black hole. First, the 2D boundary is described by a coherent spin network state in the semi-classical regime. The stationary phase approximation allows to recover in the asymptotic limit the usual amplitude for 3D quantum gravity as the character of the symmetry of asymptotically flat gravity, the BMS group. Then I introduce a new type of coherent boundary state, which allows an exact evaluation of the amplitude for 3D quantum gravity. I obtain a complex regularization of the BMS character. The possibility of this exact computation suggests the existence of a (quasi)-integrable structure, linked to the symmetries of 3D quantum gravity with 2D finite boundary.
We discuss aspects of non-perturbative unitarity in quantum field theory. The additional ghost degrees of freedom arising in truncations of an effective action at a finite order in derivatives could be fictitious degrees of freedom. Their contributio
ns to the fully-dressed propagator -- the residues of the corresponding ghost-like poles -- vanish once all operators compatible with the symmetry of the theory are included in the effective action. These fake ghosts do not indicate a violation of unitarity.
We analyze the partition function of three-dimensional quantum gravity on the twisted solid tours and the ensuing dual field theory. The setting is that of a non-perturbative model of three dimensional quantum gravity--the Ponzano-Regge model, that w
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