Three-Dimensional Gravity Revisited

By E. Witten. 2007

583 citations recorded by the source corpus.

We consider the problem of identifying the CFT's that may be dual to pure gravity in three dimensions with negative cosmological constant. The c-theorem indicates that three-dimensional pure gravity is consistent only at certain values of the coupling constant, and the relation to Chern-Simons gauge theory hints that these may be the values at which the dual CFT can be holomorphically factorized. If so, and one takes at face value the minimum mass of a BTZ black hole, then the energy spectrum of three-dimensional gravity with negative cosmological constant can be determined exactly. At the most negative possible value of the cosmological constant, the dual CFT is very likely the monster theory of Frenkel, Lepowsky, and Meurman. The monster theory may be the first in a discrete series of CFT's that are dual to three-dimensional gravity. The partition function of the second theory in the sequence can be determined on a hyperelliptic Riemann surface of any genus. We also make a similar analysis of supergravity.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/90d61c776f826f3cafaf4022b3c9533265c65e19

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Citations in the corpus

Partition functions of holographic minimal models (2011, background): “In Witten’s recent approach to 3d pure gravity [62], the bulk theory is topological, and the spectrum is empty (other than descendants) below the black hole threshold c/24.”
Higher spin black holes (2011, unknown): “BTZ black hole Before turning to generalizations, it is useful to review a few aspects of the standard BTZ black hole in this formulation; see [28,31,32] for relevant background on the ChernSimons description and the BTZ solution.”
Universal spectrum of 2d conformal field theory in the large c limit (2014, background): “Similar statements apply to other holomorphic objects such as BPS partition functions and elliptic genera in supersymmetric theories (see for example [6, 7, 8, 9]).”
Comments on Chern-Simons contact terms in three dimensions (2012, unknown): “(See for instance the discussion in [5].”
Bounding the space of holographic CFTs with chaos (2016, background): “It has been suggested that the CFT dual to pure AdS3 quantum gravity holomorphically factorizes [114].”
A theory of reparameterizations for AdS3 gravity (2018, background): “d k= 1;2;:::and includes complex saddles, then the regularized sum is sensible as a CFT partition function and in fact is equal [5] to the \extremal CFT" partition function conjectured by Witten [6]. For k= 1 there is a known CFT with this partition function, the \Monster CFT" of Frenkel, ”
Thermodynamics of higher spin black holes in AdS3 (2013, background): “This topological formulation was first introduced in [24], and its quantum aspects subsequently discussed in [25] (see [26] for a modern review).”
A universal inequality for CFT and quantum gravity (2009, background): “Such a conclusion would fit well with the results [9, 10, 6, 25].”
Quantum Gravity at a Lifshitz Point (2009, background): “ture 2 + 1, leading to a slightly diﬀerent reality condition on W, with w2 purely imaginary. There has been a recent resurgence of interest in topological massive gravity, initiated by [29]; see also [30]. – 18 – In order to compare these two theories, it is natural to express our model in relativis”
Emergent spacetime and holographic CFTs (2011, background): “Before we close this section let us mention that the constraints from modular invariance of the boundary CFT, in the context of the AdS3/CFT2 correspondence, have been recently discussed in [76], [77], [78], [79], [80], [81].”
Modular bootstrap revisited (2016, methodology): “b HFK, we have not been able to resolve their dierence numerically. 12 5 10 15 20 c -0.03 -0.02 -0.01 0.00 0.01 0.02 0.03 HFK - mod (N) Figure 5: HFK (N) mod as a function of central charge c, for c2[4;22] and increasing N. The numerical values of the HFK bound are obtained by a linear extrapolation”
Torsional anomalies, Hall viscosity, and bulk-boundary correspondence in topological states (2012, background): “The leading terms of a generic gravitational action in 3 dimensions may be written as [33]”
Nonlinear W∞ as asymptotic symmetry of three-dimensional higher spin AdS gravity (2010, methodology): “A possible holographic dual in this regime was explored recently by Witten [36] for pure AdS gravity.”
Umbral Moonshine (2012, methodology): “A notion of extremal holomorphic conformal field theory was given in [27] following earlier related work on vertex operator superalgebras in [72].”
Chiral gravity in three dimensions (2008, methodology): “Towards this end the approach of [9] may prove useful.”
AdS3 gravity and random CFT (2020, background): “dS 3 gravity Three-dimensional gravity with negative cosmological constant is often said to be classically equivalent to a Chern-Simons theory [42]. (For statements going beyond classical physics see [43,44].) This statement needs additional qualiers in order to be true. More precisely, AdS 3 gravit”