An Exploration of AdS3 Gravity as a Holographic Theory




Harvey, William

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The holographic principle is a supposed property of quantum gravity which states that the description of a volume of space can be encoded on a lower-dimensional boundary to the region. One such example is that of the Bekenstein-Hawking entropy of a black hole, which states the remarkable fact that the entropy of a black hole is simply its surface area. The most successful framework for holography is the AdS/CFT correspondence, which provides a non-perturbative formulation of string theory (and other theories of quantum gravity such as JT gravity). The purpose of this thesis is two-fold. The first is to give an overview of the AdS/CFT correspondence, including two separate historically significant applications of the correspondence. The latter application involves that of the AdS3/CFT2 correspondence, which ties into the second purpose of this thesis. (2+1)-dimensional gravity with negative cosmological constant (also known as `"pure AdS3 gravity") is exactly soluble system as a classical system, and although it is still yet undetermined if AdS3 quantum gravity is UV-complete there are still various computations one can make. In particular, this thesis considers coupling pure AdS3 gravity to a large number of light matter fields dual to relevant operators. This model has eternal traversable wormholes supported by suitable boundary conditions on the matter fields. Within this construction, the field theory of boundary gravitons is used to compute the spectrum of gravitational fluctuations and in principle the gravitational contribution to scattering processes in the wormhole.



Gravity, Holography, Duality, anti de-Sitter space, Conformal Field Theory, Quantum Gravity, AdS/CFT Correspondence, Virasoro, Eternal Traversable Wormhole, BTZ Black Hole, Boundary Graviton, Pure AdS3 Gravity, Double Trace Deformation, Spectrum of Fluctuations, Thermal AdS3, Alekseev-Shatashvili Theory