What happens due to the baby universe effect in JT gravity? -Analysis of correlation functions and ERB length at late time using three approaches-

Abstract

We analyze the correlation function in JT gravity using three approaches: by summing over all geodesics connecting boundary operators, integrating over the region of moduli space determined by the ``no-shortcut condition'' introduced by D.Stanford and Z.Yang, and using the formula for the universal spectral density correlation in the $\tau$-scaling limit. We find that the behaviors of the three results coincide at late times: they all exhibit a ``ramp'' instead of permanent decay. Using the third approach we also confirm that the ``plateau'' appears after $T_H=2\pi e^{S_0}{\hat{\rho }}_0(E)$. Overall, our results are consistent with the SFF analysis. We also calculate the ERB length $⟨\ell (T)⟩$ using the three approaches and find that the results are in good agreement with each other. We also find that the $⟨\ell (T)⟩$ grows as a cubic function in $T$ due to the contribution from geometry including one observable baby universe, and converges to a constant after $T=T_H$. For the geometry with one baby universe, we compute the size $⟨b(T)⟩$ of the baby universe and find that it is of the same order as $⟨\ell (T)⟩$. This result is consistent with the baby universe emission mechanism claimed by P.Saad.

arXiv comment30pages,10figures

References in corpus (20)

• Gapless Spin-Fluid Ground State in a Random Quantum Heisenberg Magnet
• Comments on the Sachdev-Ye-Kitaev model
• Eternal Black Holes in AdS
• Quasinormal Modes of AdS Black Holes and the Approach to Thermal Equilibrium
• The Spectrum in the Sachdev-Ye-Kitaev Model
• Black Holes and Random Matrices
• The soft mode in the Sachdev-Ye-Kitaev model and its gravity dual
• Wormholes in AdS
• Fermionic Localization of the Schwarzian Theory
• Disturbing Implications of a Cosmological Constant
• Solving the Schwarzian via the Conformal Bootstrap
• The Trouble with de Sitter Space
• Euclidean Wormholes in String Theory
• All point correlation functions in SYK
• Very Long Time Scales and Black Hole Thermal Equilibrium
• Shockwave S-matrix from Schwarzian Quantum Mechanics
• Developments in Topological Gravity
• The Case of the Missing Gates: Complexity of Jackiw-Teitelboim Gravity
• Clocks and Rods in Jackiw-Teitelboim Quantum Gravity
• An integrable road to a perturbative plateau

Cited by in corpus (1)

• Universal Time Evolution of Holographic and Quantum Complexity