Instanton effects vs resurgence in the $O(3)$ sigma model

Abstract

We investigate the ground-state energy of the integrable two dimensional $O(3)$ sigma model in a magnetic field. By determining a large number of perturbative coefficients we explore the closest singularities of the corresponding Borel function. We then confront its median resummation to the high precision numerical solution of the exact integral equation and observe that the leading exponentially suppressed contribution is not related to the asymptotics of the perturbative coefficients. By analytically expanding the integral equation we calculate the leading non-perturbative contributions up to fourth order and find complete agreement. These anomalous terms could be attributed to instantons, while the asymptotics of the perturbative coefficients seems to be related to renormalons.

arXiv comment8 pages, 2 figures

References in corpus (11)

• Renormalons
• Lectures on non-perturbative effects in large N gauge theories, matrix models and strings
• A Primer on Resurgent Transseries and Their Asymptotics
• An Introduction to Resurgence, Trans-Series and Alien Calculus
• Nonperturbative Ambiguities and the Reality of Resurgent Transseries
• Quantum integrability and functional equations
• From the mass gap in O(N) to the non-Borel-summability in O(3) and O(4) sigma-models
• The Resurgence of the Cusp Anomalous Dimension
• Renormalons in integrable field theories
• From perturbative to non-perturbative in the O(4) sigma model
• Resurgence and $1/N$ Expansion in Integrable Field Theories

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• Resurgence and semiclassical expansion in two-dimensional large-$N$ sigma models
• All-order Resurgence from Complexified Path Integral in a Quantum Mechanical System with Integrability
• Resurgence in 2-dimensional Yang-Mills and a genus altering deformation
• Resurgence in the Scalar Quantum Electrodynamics Euler-Heisenberg Lagrangian
• Asymptotics in the bi-Yang-Baxter Sigma Model