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arXiv · 2412.20398

Jackiw-Teitelboim Gravity and Lorentzian Quantum Cosmology

Masazumi Honda·Hiroki Matsui·Kota Numajiri·Kazumasa Okabayashi
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Abstract

We directly evaluate the probability amplitudes in Jackiw-Teitelboim (JT) gravity using the Lorentzian path integral formulation. By imposing boundary conditions on the scale factor and the dilaton field, the Lorentzian path integral uniquely yields the probability amplitude without contradiction. Under Dirichlet boundary conditions, we demonstrate that the amplitude derived from the Lorentzian path integral is expressed in terms of the modified Bessel function of the second kind. Furthermore, we provide the determinant for various boundary conditions and perform a detailed analysis of the Lefschetz thimble structure and saddle points. In contrast to four-dimensional gravity, we show that the Hartle-Hawking no-boundary proposal is approximately valid in JT quantum cosmology. Furthermore, addressing quantum perturbation issues, we show that the quantum genesis of the two-dimensional universe occurs and exhibits perturbative regularity when the dilaton field is non-zero and large as an initial condition.

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Masazumi Honda, Hiroki Matsui, Kota Numajiri, Kazumasa Okabayashi. 2024-12-29. Jackiw-Teitelboim Gravity and Lorentzian Quantum Cosmology. https://doi.org/10.1103/vrcy-y61l

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