Jackiw-Teitelboim Gravity and Lorentzian Quantum Cosmology
arXiv:2412.20398 · doi:10.1103/vrcy-y61l
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.
18 pages, 4 figures
References in corpus (42)
- Chaos in AdS holography
- An Investigation of AdS Backreaction and Holography
- Fermionic Localization of the Schwarzian Theory
- Lorentzian Quantum Cosmology
- Solvable Models of Quantum Black Holes: A Review on Jackiw-Teitelboim Gravity
- On the Dynamics of Near-Extremal Black Holes
- No smooth beginning for spacetime
- Low-dimensional de Sitter quantum gravity
- No Rescue for the No Boundary Proposal
- The Real No-Boundary Wave Function in Lorentzian Quantum Cosmology
- Tunneling wave function of the universe
- A note on perturbation series in supersymmetric gauge theories
- Review of the No-Boundary Wave Function
- The No-Boundary Proposal as a Path Integral with Robin Boundary Conditions
- Damped perturbations in the no-boundary state
- What is the No-Boundary Wave Function of the Universe?
- No-boundary prescriptions in Lorentzian quantum cosmology
- Tunneling wave function of the universe II: the backreaction problem
- Borel summability of perturbative series in 4d N=2 and 5d N=1 theories
- Loops rescue the no-boundary proposal
- How to resum perturbative series in 3d N=2 Chern-Simons matter theories
- The no-boundary proposal in biaxial Bianchi IX minisuperspace
- Quantum tunnelling, real-time dynamics and Picard-Lefschetz thimbles
- The Wave Function of Simple Universes, Analytically Continued From Negative to Positive Potentials
- Is Action Complexity better for de Sitter space in Jackiw-Teitelboim gravity?
- Existence of real time quantum path integrals
- JT Gravity in de Sitter Space and the Problem of Time
- Unstable no-boundary fluctuations from sums over regular metrics
- Two Wave Functions and dS/CFT on S^1 x S^2
- On Gauss-bonnet gravity and boundary conditions in Lorentzian path-integral quantization
- Jackiw-Teitelboim and Kantowski-Sachs quantum cosmology
- Aspects of AdS holography with non-constant dilaton
- Vacuum decay in the Lorentzian path integral
- Lorentzian path integral for quantum tunneling and WKB approximation for wave-function
- Surprises in Lorentzian path-integral of Gauss-Bonnet gravity
- No Smooth Spacetime in Lorentzian Quantum Cosmology and Trans-Planckian Physics
- Resurgence in Lorentzian quantum cosmology: No-boundary saddles and resummation of quantum gravity corrections around tunneling saddle points
- Resumming perturbative series in the presence of monopole bubbling effects
- Lorentzian Robin Universe of Gauss-Bonnet Gravity
- Hartle-Hawking No-boundary Proposal and Hořava-Lifshitz Gravity
- No smooth spacetime: Exploring primordial perturbations in Lorentzian quantum cosmology
- Remote Hawking-Moss instanton and the Lorentzian path integral