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Quantum gravity partition functions in three dimensions

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Abstract

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.

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Authors and Affiliations

  1. McGill Physics Department, 3600 rue University, Montréal, QC, H3A 2T8, Canada

    Alexander Maloney

  2. School of Natural Sciences, Institute for Advanced Study, Einstein Dr., Princeton, NJ, 08540, U.S.A.

    Edward Witten

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  1. Alexander Maloney
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  2. Edward Witten
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Correspondence to Alexander Maloney.

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ArXiv ePrint: 0712.0155

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Maloney, A., Witten, E. Quantum gravity partition functions in three dimensions. J. High Energ. Phys. 2010, 29 (2010). https://doi.org/10.1007/JHEP02(2010)029

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