Large-order Perturbation Theory and de Sitter/Anti de Sitter Effective Actions

Abstract

We analyze the large-order behavior of the perturbative weak-field expansion of the effective Lagrangian density of a massive scalar in de Sitter and anti de Sitter space, and show that this perturbative information is not sufficient to describe the non-perturbative behavior of these theories, in contrast to the analogous situation for the Euler-Heisenberg effective Lagrangian density for charged scalars in constant electric and magnetic background fields. For example, in even dimensional de Sitter space there is particle production, but the effective Lagrangian density is nevertheless real, even though its weak-field expansion is a divergent non-alternating series whose formal imaginary part corresponds to the correct particle production rate. This apparent puzzle is resolved by considering the full non-perturbative structure of the relevant Feynman propagators, and cannot be resolved solely from the perturbative expansion.

arXiv comment18 pages

References in corpus (10)

• Conformal Vacua and Entropy in de Sitter Space
• Heisenberg-Euler Effective Lagrangians : Basics and Extensions
• Les Houches Lectures on De Sitter Space
• Borel Summation of the Derivative Expansion and Effective Actions
• Effective action in spherical domains
• The Barnes zeta-function, sphere determinants and Glaisher- Kinkelin-Bendersky constants
• Can Asymptotic Series Resolve the Problems of Inflation?
• Massive-Scalar Effective Actions on Anti-de Sitter Spacetime
• Functional determinants on spheres and sectors
• Large Order Behavior of Quasiclassical Euclidean Gravity in Minisuperspace Models

Cited by in corpus (19)

• Resurgence and Trans-series in Quantum Field Theory: The CP(N-1) Model
• Partition functions and double-trace deformations in AdS/CFT
• Super-Adiabatic Particle Number in Schwinger and de Sitter Particle Production
• The Holographic Universe
• Schwinger Pair Production in dS_2 and AdS_2
• Cosmological 3-point correlators from holography
• Gravitational corrections to the Euler-Heisenberg Lagrangian
• Real or Imaginary? (On pair creation in de Sitter space)
• Pseudo-Supersymmetry and the Domain-Wall/Cosmology Correspondence
• Some series and integrals involving the Riemann zeta function, binomial coefficients and the harmonic numbers. Volume I
• Propagators and Gaussian effective actions in various patches of de Sitter space
• Determinants and conformal anomalies of GJMS operators on spheres
• Free energy and entropy in Rindler and de Sitter space-times
• On partition functions and phases of scalars in AdS
• Complex effective actions and gravitational pair creation
• Vacuum fermionic currents in braneworld models on AdS bulk with a cosmic string
• A Gauge-Gravity Relation in the One-loop Effective Action
• Probing the Vacuum Structure of Spacetime
• On (dis)agreement between different methods of calculation of the imaginary part of the effective action in expanding space-times