Pure gravity on AdS3 is dual to a conformal field theory.
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Peer-reviewed literature discusses the theoretical formulation of pure 3D gravity and its path integrals in AdS3 spaces in relation to conformal field theory interpretations, but whether pure gravity on AdS3 is rigorously dual to a conformal field theory remains an open question under active investigation rather than being fully established.
Abstract General relativity in three spacetime dimensions is a simplified model of gravity, possessing no local degrees of freedom, yet rich enough to admit black-hole solutions and other phenomena of interest. In the presence of a negative cosmological constant, the asymptotically anti–de Sitter (AdS) solutions admit a symmetry algebra consisting of two copies of the Virasoro algebra, with central charge inversely proportional to Newton’s constant. The study of this theory is greatly enriched by the AdS/CFT correspondence, which in this case implies a relationship to two-dimensional conformal field theory. General aspects of this theory can be understood by focusing on universal properties such as symmetries. The best understood examples of the AdS3/CFT2 correspondence arise from string theory constructions, in which case the gravity sector is accompanied by other propagating degrees of freedom. A question of recent interest is whether pure gravity can be made sense of as a quantum theory of gravity with a holographic dual. Attempting to answer this question requires making sense of the path integral over asymptotically AdS3 geometries.
On a Canonical Quantization of 3D Anti de Sitter Pure Gravity : Jihun Kim : Free Download, Borrow, and Streaming : Internet Archive Skip to main content Keep the news in the Wayback Machine. Sign Fight for the Future's letter .
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Favorite Share Flag Flag this item for Graphic Violence Explicit Sexual Content Hate Speech Misinformation/Disinformation Marketing/Phishing/Advertising Misleading/Inaccurate/Missing Metadata texts On a Canonical Quantization of 3D Anti de Sitter Pure Gravity by Jihun Kim ; Massimo Porrati Publication date 2015-08-14 Usage http://arxiv.org/licenses/nonexclusive-distrib/1.0/ Topics High Energy Physics - Theory Publisher arXiv.org Collection arxiv ; journals Contributor Internet Archive Language English Item Size 35.3M We perform a canonical quantization of pure gravity on AdS3 using as a technical tool its equivalence at the classical level with a Chern-Simons theory with gauge group SL(2,R)xSL(2,R).
We first quantize the theory canonically on an asymptotically AdS space --which is topologically the real line times a Riemann surface with one connected boundary. Using the "constrain first" approach we reduce canonical quantization to quantization of orbits of the Virasoro group and Kaehler quantization of Teichmuller space. After explicitly computing the Kaehler form for the torus with one boundary component and after extending that result to higher genus, we recover known results, such as that wave functions of SL(2,R) Chern-Simons theory are conformal blocks.
We find new restrictions on the Hilbert space of pure gravity by imposing invariance under large diffeomorphisms and normalizability of the wave function. The Hilbert space of pure gravity is shown to be the target space of Conformal Field Theories with continuous spectrum and a lower bound on operator dimensions. A projection defined by topology changing amplitudes in Euclidean gravity is proposed. It defines an invariant subspace that allows for a dual interpretation in terms of a Liouville CFT. Problems and features of the CFT dual are assessed and a new definition of the Hilbert space, exempt from those problems, is proposed in the case of highly-curved AdS3. Notes 61 pages, 7 figures.
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