Quantum gravity partition functions in three dimensions
By A. Maloney, E. Witten. 2007
598 citations recorded by the source corpus.
We consider pure three-dimensional quantum gravity with a negative cosmological constant. The sum of known contributions to the partition function from classical geometries can be computed exactly, including quantum corrections. However, the result is not physically sensible, and if the model does exist, there are some additional contributions. One possibility is that the theory may have long strings and a continuous spectrum. Another possibility is that complex geometries need to be included, possibly leading to a holomorphically factorized partition function. We analyze the subleading corrections to the Bekenstein-Hawking entropy and show that these can be correctly reproduced in such a holomorphically factorized theory. We also consider the Hawking-Page phase transition between a thermal gas and a black hole and show that it is a phase transition of Lee-Yang type, associated with a condensation of zeros in the complex temperature plane. Finally, we analyze pure three-dimensional supergravity, with similar results.
Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/b4e3df69b946aa59b6eb5de651598dd06bb6babd
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Astronomy and Astrophysics
In Nuclear and High Energy Physics
In Statistical and Nonlinear Physics
Citations in the corpus
- Instability in cosmological topologically massive gravity at the chiral point (2008, methodology): “The considerations in the previous paragraphs might be of interest for the Euclidean approach/CFT approach pursued in [42–50].”
- Higher spin AdS3 supergravity and its dual CFT (2011, unknown): “The dual theory should be an N = (1, 1) superconformal field theory in two dimensions, and the partition function of the Chern-Simons theory was proposed in [32] by making use of the boundary degrees of freedom.”
- Holographic entanglement beyond classical gravity (2013, background): “The one-loop correction is perturbatively exact in pure three dimensional gravity [7].”
- Universal spectrum of 2d conformal field theory in the large c limit (2014, background): “Maximizing this expression over SL(2, Z) images leads to an intricate Euclidean phase diagram with an infinite number of phases tessellating the upper half τ -plane [6, 24, 27].”
- Chiral gravity in three dimensions (2008, methodology): “Indeed discrepancies with the semiclassical analysis mentioned in [9]-[16] disappear for the special case kL = 0.”
- The factorization problem in Jackiw-Teitelboim gravity (2018, background): “ected space. These conjectures are consistent with the results of Maloney and Witten, who computed the one-boundary partition function exactly and saw that it did not have the form of a thermal trace [67].19 There has been a fair bit of worry about how to \x" this, for example by including comp”
- Minimal model holography (2012, background): “This generalizes the expression for the case of pure gravity (s = 2) [96], as explicitly checked in [66].”
- Analytic continuation of Liouville theory (2011, background): “Secondly, in three-dimensional Euclidean quantum gravity with negative cosmological constant, it was found in [53] that including only real smooth solutions in the path integral produces a partition function that does not have the correct form to come from a CFT computation.”
- Umbral Moonshine (2012, methodology): “We refer to [28, 29, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85] for further discussions on the AdS/CFT correspondence and extremal CFT’s.”
- Partition functions of holographic minimal models (2011, background): “Since the higher spin theory also contains standard BTZ black holes, the usual Farey tail picture [63, 64, 65] suggests that CFT states above the black hole threshold might be obtained from the perturbative part of the spectrum upon applying modular transformations.”
- Chiral gravity, log gravity, and extremal CFT (2009, methodology): “The computation proceeds exactly as in [31], so we refer the reader there for details.”
- The statistical mechanics of near-BPS black holes (2020, unknown): “In the bosonic case, the path integral of pure gravity including quantum fluctuations around this geometry can be exactly computed and it is one-loop exact [101].”
- Entanglement Entropy at Large Central Charge (2013, background): “Note that this does not mean quantum Liouville theory is equivalent to either gravity or the CFT (see [42, 43] for obstacles to this interpretation).”