Interpolating function and Stokes Phenomena

Abstract

When we have two expansions of physical quantity around two different points in parameter space, we can usually construct a family of functions, which interpolates the both expansions. In this paper we study analytic structures of such interpolating functions and discuss their physical implications. We propose that the analytic structures of the interpolating functions provide information on analytic property and Stokes phenomena of the physical quantity, which we approximate by the interpolating functions. We explicitly check our proposal for partition functions of zero-dimensional ${\phi }^4$ theory and Sine-Gordon model. In the zero dimensional Sine-Gordon model, we compare our result with a recent result from resurgence analysis. We also comment on construction of interpolating function in Borel plane.

21+6 pages, 16 figures; v2: minor corrections; v3: minor corrections

References in corpus (7)

• Resurgence and the Nekrasov-Shatashvili Limit: Connecting Weak and Strong Coupling in the Mathieu and Lam'e Systems
• High and Low Dimensions in The Black Hole Negative Mode
• Finite N from Resurgent Large N
• Resurgence and Holomorphy: From Weak to Strong Coupling
• On Perturbation theory improved by Strong coupling expansion
• Decoding perturbation theory using resurgence: Stokes phenomena, new saddle points and Lefschetz thimbles
• Resurgent Analysis of Localizable Observables in Supersymmetric Gauge Theories

Cited by in corpus (9)

• A Primer on Resurgent Transseries and Their Asymptotics
• Resurgence in sine-Gordon quantum mechanics: Exact agreement between multi-instantons and uniform WKB
• Non-BPS exact solutions and their relation to bions in $\mathbb{C}{P}^{N-1}$ models
• Quantum phase transition and Resurgence: Lessons from 3d $\mathcal{N}=4$ SQED
• From weak to strong: constrained extrapolation of perturbation series with applications to dilute Fermi systems
• S-duality invariant perturbation theory improved by holography
• Constrained extrapolation problem and order-dependent mappings
• Monopoles, Clarified
• On interpolating anomalous dimension of twist-two operators with general spins