(2+1)-Dimensional Gravity as an Exactly Soluble System
TL;DR: By disentangling the hamiltonian constraint equations, 2 + 1 dimensional gravity (with or without a cosmological constant) is shown to be exactly soluble at the classical and quantum levels.
About: This article is published in Nuclear Physics.The article was published on 1988-12-19. It has received 2636 citations till now. The article focuses on the topics: Quantum gravity & Spin foam.
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TL;DR: In this paper, the holographic correspondence between field theories and string/M theory is discussed, focusing on the relation between compactifications of string theory on anti-de Sitter spaces and conformal field theories.
5,610 citations
Cites background from "(2+1)-Dimensional Gravity as an Exa..."
...In higher dimensions this is not possible since pure gravity is not renormalizable, so the only known sensible quantum gravity theory is string theory, but in three dimensions gravity can be rewritten as a Chern}Simons theory [480,481], and this theory is renormalizable....
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TL;DR: In this paper, it was shown that 2+1 dimensional quantum Yang-Mills theory with an action consisting purely of the Chern-Simons term is exactly soluble and gave a natural framework for understanding the Jones polynomial of knot theory in three dimensional terms.
Abstract: It is shown that 2+1 dimensional quantum Yang-Mills theory, with an action consisting purely of the Chern-Simons term, is exactly soluble and gives a natural framework for understanding the Jones polynomial of knot theory in three dimensional terms. In this version, the Jones polynomial can be generalized fromS
3 to arbitrary three manifolds, giving invariants of three manifolds that are computable from a surgery presentation. These results shed a surprising new light on conformal field theory in 1+1 dimensions.
5,093 citations
TL;DR: The holographic principle as mentioned in this paper asserts that the fundamental degrees of freedom involved in a unified description of spacetime and matter must be manifest in an underlying quantum theory of gravity, and it has yet to be explained.
Abstract: There is strong evidence that the area of any surface limits the information content of adjacent spacetime regions, at $1.4\ifmmode\times\else\texttimes\fi{}{10}^{69}$ bits per square meter. This article reviews the developments that have led to the recognition of this entropy bound, placing special emphasis on the quantum properties of black holes. The construction of light sheets, which associate relevant spacetime regions to any given surface, is discussed in detail. This article explains how the bound is tested, and its validity is demonstrated in a wide range of examples. A universal relation between geometry and information is thus uncovered. It has yet to be explained. The holographic principle asserts that its origin must lie in the number of fundamental degrees of freedom involved in a unified description of spacetime and matter. It must be manifest in an underlying quantum theory of gravity. This article surveys some successes and challenges in implementing the holographic principle.
1,706 citations
Cites background from "(2+1)-Dimensional Gravity as an Exa..."
...An effectively lower-dimensional description is evident in the quantum gravity of 2 + 1 dimensional spacetimes (Witten, 1988; see also van Nieuwenhuizen, 1985; Achucarro and Townsend, 1986; Brown and Henneaux, 1986....
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TL;DR: In this article, a holographic duality is proposed relating quantum gravity on dSD (D-dimensional de Sitter space) to conformal field theory on a single SD−1 ((D-1)-sphere), in which bulk de Sitters correlators with points on the boundary are related to CFT correlators on the sphere, and points on + (the future boundary of dSD) are mapped to the antipodal points on SD− 1 relative to those on − for the case of dS3, which is analyzed in some detail, the central charge of
Abstract: A holographic duality is proposed relating quantum gravity on dSD (D-dimensional de Sitter space) to conformal field theory on a single SD−1 ((D-1)-sphere), in which bulk de Sitter correlators with points on the boundary are related to CFT correlators on the sphere, and points on + (the future boundary of dSD) are mapped to the antipodal points on SD−1 relative to those on − For the case of dS3, which is analyzed in some detail, the central charge of the CFT2 is computed in an analysis of the asymptotic symmetry group at ± This dS/CFT proposal is supported by the computation of correlation functions of a massive scalar field In general the dual CFT may be non-unitary and (if for example there are sufficently massive stable scalars) contain complex conformal weights We also consider the physical region − of dS3 corresponding to the causal past of a timelike observer, whose holographic dual lives on a plane rather than a sphere − can be foliated by asymptotically flat spacelike slices Time evolution along these slices is generated by L0+0, and is dual to scale transformations in the boundary CFT2
1,377 citations
Cites background from "(2+1)-Dimensional Gravity as an Exa..."
...The closest things we have at present to examples are Hull’s spacelike D-branes [8,13] and Chern-Simon de Sitter gravity [27,28]....
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TL;DR: In this article, the authors define the conditions generales d'utilisation of commercial or impression systematique as constitutive of an infraction penale, i.e., the copie ou impression de ce fichier doit contenir la presente mention de copyright.
Abstract: © Publications mathematiques de l’I.H.E.S., 1988, tous droits reserves. L’acces aux archives de la revue « Publications mathematiques de l’I.H.E.S. » (http://www. ihes.fr/IHES/Publications/Publications.html), implique l’accord avec les conditions generales d’utilisation (http://www.numdam.org/legal.php). Toute utilisation commerciale ou impression systematique est constitutive d’une infraction penale. Toute copie ou impression de ce fichier doit contenir la presente mention de copyright.
900 citations
Cites background from "(2+1)-Dimensional Gravity as an Exa..."
...Witten has recently considered [15] a Ghern-Simons theory for the non-compact group SL(2, C) in relation with gravitational theories in (2 + 1)-dimensions, and hence with hyperbolic 3-manifolds....
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References
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TL;DR: In this paper, it was shown that 2+1 dimensional quantum Yang-Mills theory with an action consisting purely of the Chern-Simons term is exactly soluble and gave a natural framework for understanding the Jones polynomial of knot theory in three dimensional terms.
Abstract: It is shown that 2+1 dimensional quantum Yang-Mills theory, with an action consisting purely of the Chern-Simons term, is exactly soluble and gives a natural framework for understanding the Jones polynomial of knot theory in three dimensional terms. In this version, the Jones polynomial can be generalized fromS
3 to arbitrary three manifolds, giving invariants of three manifolds that are computable from a surgery presentation. These results shed a surprising new light on conformal field theory in 1+1 dimensions.
5,093 citations
TL;DR: A twisted version of four dimensional supersymmetric gauge theory is formulated in this paper, which refines a nonrelativistic treatment by Atiyah and appears to underlie many recent developments in topology of low dimensional manifolds; the Donaldson polynomial invariants of four manifolds and the Floer groups of three manifolds appear naturally.
Abstract: A twisted version of four dimensional supersymmetric gauge theory is formulated. The model, which refines a nonrelativistic treatment by Atiyah, appears to underlie many recent developments in topology of low dimensional manifolds; the Donaldson polynomial invariants of four manifolds and the Floer groups of three manifolds appear naturally. The model may also be interesting from a physical viewpoint; it is in a sense a generally covariant quantum field theory, albeit one in which general covariance is unbroken, there are no gravitons, and the only excitations are topological.
2,568 citations
TL;DR: In this article, the authors analyzed three-dimensional Yang-Mills and gravity theories augmented by gauge-invariant mass terms and quantized a dimensionless mass-couplingconstant ratio.
Abstract: Three-dimensional Yang-Mills and gravity theories augmented by gauge-invariant mass terms are analyzed. These topologically nontrivial additions profoundly alter the particle content of the models and lead to quantization of a dimensionless mass-coupling-constant ratio. The vector field excitations become massive, with spin 1 (rather than massless with spin 0), and the mass provides an infrared cutoff. The gravitation acquires mass, mediates finite-range interactions, and has spin 2 (rather than being absent altogether); although its mass term is of third derivative order, there are no ghosts or acausalities.
1,693 citations
TL;DR: A Hamiltonian formulation of general relativity based on certain spinorial variables is introduced that enables one to imbed the constraint surface in the phase space of Einstein's theory into that of Yang-Mills theory.
Abstract: A Hamiltonian formulation of general relativity based on certain spinorial variables is introduced. These variables simplify the constraints of general relativity considerably and enable one to imbed the constraint surface in the phase space of Einstein's theory into that of Yang-Mills theory. The imbedding suggests new ways of attacking a number of problems in both classical and quantum gravity. Some illustrative applications are discussed.
1,523 citations
TL;DR: In this article, a geometrie symplectique des fibres cotangents aux espaces de modules de fibres vectoriels stables sur a surface de Riemann is considered.
Abstract: On considere la geometrie symplectique des fibres cotangents aux espaces de modules de fibres vectoriels stables sur une surface de Riemann. On montre que ce sont des systemes dynamiques hamiltoniens algebriquement completement integrables
1,031 citations