Resurgence in Lorentzian quantum cosmology: No-boundary saddles and resummation of quantum gravity corrections around tunneling saddle points

Abstract

We revisit the path-integral approach to the wave function of the Universe by utilizing Lefschetz thimble analyses and resurgence theory. The traditional Euclidean path-integral of gravity has the notorious ambiguity of the direction of Wick rotation. In contrast, the Lorentzian method can be formulated concretely with the Picard-Lefschetz theory. Yet, a challenge remains: the physical parameter space lies on a Stokes line, meaning that the Lefschetz-thimble structure is still unclear. Through complex deformations, we resolve this issue by uniquely identifying the thimble structure. This leads to the tunneling wave function, as opposed to the no-boundary wave function, offering a more rigorous proof of the previous results. Further exploring the parameter space, we discover rich structures: the ambiguity of the Borel resummation of perturbative series around the tunneling saddle points is exactly canceled by the ambiguity of the contributions from no-boundary saddle points. This indicates that resurgence also works in quantum cosmology, particularly in the minisuperspace model.

14 pages, 7 figures, v3: we corrected minor typos in equations in the introduction and Section. IV

References in corpus (38)

• Open string amplitudes and large order behavior in topological string theory
• Nonperturbative effects and nonperturbative definitions in matrix models and topological strings
• No Rescue for the No Boundary Proposal
• The Real No-Boundary Wave Function in Lorentzian Quantum Cosmology
• Structure of Lefschetz thimbles in simple fermionic systems
• Resurgent Transseries and the Holomorphic Anomaly: Nonperturbative Closed Strings in Local CP2
• Exact properties of an integrated correlator in $\mathcal{N}=4$ $SU(N)$ SYM
• Neutral bions in the $\mathbb{C}{P}^{N-1}$ model
• Review of the No-Boundary Wave Function
• The No-Boundary Proposal as a Path Integral with Robin Boundary Conditions
• Resumming the string perturbation series
• IR Renormalons vs. Operator Product Expansion in Supersymmetric and Related Gauge Theories
• Finite N from Resurgent Large N
• Nonperturbative effects and resurgence in JT gravity at finite cutoff
• Resurgence of the large-charge expansion
• The no-boundary proposal in biaxial Bianchi IX minisuperspace
• The Wave Function of Simple Universes, Analytically Continued From Negative to Positive Potentials
• Transasymptotics and hydrodynamization of the Fokker-Planck equation for gluons
• New renormalons from analytic trans-series
• From perturbative to non-perturbative in the O(4) sigma model
• Existence of real time quantum path integrals
• Testing the Bethe ansatz with large N renormalons
• On Gauss-bonnet gravity and boundary conditions in Lorentzian path-integral quantization
• Picard-Lefschetz decomposition and Cheshire Cat resurgence in 3D $\mathcal{N}=2$ field theories
• Jackiw-Teitelboim and Kantowski-Sachs quantum cosmology
• Lorentzian path integral for quantum tunneling and WKB approximation for wave-function
• Vacuum decay in the Lorentzian path integral
• Surprises in Lorentzian path-integral of Gauss-Bonnet gravity
• Semiclassical Trans-Series from the Perturbative Hopf-Algebraic Dyson-Schwinger Equations: ${\varphi }^3$ QFT in 6 Dimensions
• No Smooth Spacetime in Lorentzian Quantum Cosmology and Trans-Planckian Physics
• To the cusp and back: Resurgent analysis for modular graph functions
• Instantons, renormalons and the theta angle in integrable sigma models
• Quantum phase transition and Resurgence: Lessons from 3d $\mathcal{N}=4$ SQED
• Hartle-Hawking No-boundary Proposal and Hořava-Lifshitz Gravity
• Resurgent Analysis of SU(2) Chern-Simons Partition Function on Brieskorn Spheres $\Sigma (2,3,6n+5)$
• No smooth spacetime: Exploring primordial perturbations in Lorentzian quantum cosmology
• Resurgence of one-point functions in a matrix model for 2D type IIA superstrings
• Resurgent Structure of the Topological String and the First Painlevé Equation

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