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Liouville quantum gravity : holography, JT and matrices

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Abstract
We study two-dimensional Liouville gravity and minimal string theory on spaces with fixed length boundaries. We find explicit formulas describing the gravitational dressing of bulk and boundary correlators in the disk. Their structure has a striking resemblance with observables in 2d BF (plus a boundary term), associated to a quantum deformation of SL(2, ), a connection we develop in some detail. For the case of the (2, p) minimal string theory, we compare and match the results from the continuum approach with a matrix model calculation, and verify that in the large p limit the correlators match with Jackiw-Teitelboim gravity. We consider multi-boundary amplitudes that we write in terms of gluing bulk one-point functions using a quantum deformation of the Weil-Petersson volumes and gluing measures. Generating functions for genus zero Weil-Petersson volumes are derived, taking the large p limit. Finally, we present preliminary evidence that the bulk theory can be interpreted as a 2d dilaton gravity model with a sinh Phi dilaton potential.
Keywords
Conformal Field Theory, Matrix Models, Models of Quantum Gravity, Quantum Groups, WEIL-PETERSSON VOLUMES, CONFORMAL FIELD-THEORY, FUSION RULES, BOUNDARY, 2D, QUANTIZATION, LOOPS, REPRESENTATIONS, CORRELATORS, GEOMETRY

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MLA
Mertens, Thomas, and Gustavo J. Turiaci. “Liouville Quantum Gravity : Holography, JT and Matrices.” JOURNAL OF HIGH ENERGY PHYSICS, vol. 2021, no. 1, 2021, doi:10.1007/jhep01(2021)073.
APA
Mertens, T., & Turiaci, G. J. (2021). Liouville quantum gravity : holography, JT and matrices. JOURNAL OF HIGH ENERGY PHYSICS, 2021(1). https://doi.org/10.1007/jhep01(2021)073
Chicago author-date
Mertens, Thomas, and Gustavo J. Turiaci. 2021. “Liouville Quantum Gravity : Holography, JT and Matrices.” JOURNAL OF HIGH ENERGY PHYSICS 2021 (1). https://doi.org/10.1007/jhep01(2021)073.
Chicago author-date (all authors)
Mertens, Thomas, and Gustavo J. Turiaci. 2021. “Liouville Quantum Gravity : Holography, JT and Matrices.” JOURNAL OF HIGH ENERGY PHYSICS 2021 (1). doi:10.1007/jhep01(2021)073.
Vancouver
1.
Mertens T, Turiaci GJ. Liouville quantum gravity : holography, JT and matrices. JOURNAL OF HIGH ENERGY PHYSICS. 2021;2021(1).
IEEE
[1]
T. Mertens and G. J. Turiaci, “Liouville quantum gravity : holography, JT and matrices,” JOURNAL OF HIGH ENERGY PHYSICS, vol. 2021, no. 1, 2021.
@article{8690505,
  abstract     = {{We study two-dimensional Liouville gravity and minimal string theory on spaces with fixed length boundaries. We find explicit formulas describing the gravitational dressing of bulk and boundary correlators in the disk. Their structure has a striking resemblance with observables in 2d BF (plus a boundary term), associated to a quantum deformation of SL(2, ), a connection we develop in some detail. For the case of the (2, p) minimal string theory, we compare and match the results from the continuum approach with a matrix model calculation, and verify that in the large p limit the correlators match with Jackiw-Teitelboim gravity. We consider multi-boundary amplitudes that we write in terms of gluing bulk one-point functions using a quantum deformation of the Weil-Petersson volumes and gluing measures. Generating functions for genus zero Weil-Petersson volumes are derived, taking the large p limit. Finally, we present preliminary evidence that the bulk theory can be interpreted as a 2d dilaton gravity model with a sinh Phi dilaton potential.}},
  articleno    = {{73}},
  author       = {{Mertens, Thomas and Turiaci, Gustavo J.}},
  issn         = {{1029-8479}},
  journal      = {{JOURNAL OF HIGH ENERGY PHYSICS}},
  keywords     = {{Conformal Field Theory,Matrix Models,Models of Quantum Gravity,Quantum Groups,WEIL-PETERSSON VOLUMES,CONFORMAL FIELD-THEORY,FUSION RULES,BOUNDARY,2D,QUANTIZATION,LOOPS,REPRESENTATIONS,CORRELATORS,GEOMETRY}},
  language     = {{eng}},
  number       = {{1}},
  pages        = {{71}},
  title        = {{Liouville quantum gravity : holography, JT and matrices}},
  url          = {{http://doi.org/10.1007/jhep01(2021)073}},
  volume       = {{2021}},
  year         = {{2021}},
}

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