Resurgence in the O(4) sigma model

• Main Authors: Michael C. Abbott, Zoltán Bajnok, János Balog, Árpád Hegedűs, Saeedeh Sadeghian
• Format: Article
• Language: English
• Published: SpringerOpen 2021-05-01
• Series: Journal of High Energy Physics
• Subjects: Integrable Field Theories; Renormalization Regularization and Renormalons; Sigma Models; Field Theories in Lower Dimensions
• Online Access: https://doi.org/10.1007/JHEP05(2021)253

Abstract We analyze the free energy of the integrable two dimensional O(4) sigma model in a magnetic field. We use Volin’s method to extract high number (2000) of perturbative coefficients with very high precision. The factorial growth of these coefficients are regulated by switching to the Borel transform, where we perform several asymptotic analysis. High precision data allowed to identify Stokes constants and alien derivatives with exact expressions. These reveal a nice resurgence structure which enables to formulate the first few terms of the ambiguity free trans-series. We check these results against the direct numerical solution of the exact integral equation and find complete agreement.