From perturbative to non-perturbative in the O(4) sigma model
Michael C. Abbott, Zoltán Bajnok, János Balog, Árpád Hegedűs
Abstract
We study the resurgent trans-series for the free energy of the two-dimensional O(4) sigma model in a magnetic field. Exploiting integrability, we obtain very high-order perturbative data, from which we can explore non-perturbative sectors. We are able to determine exactly the leading real-valued exponentially small terms, which we check against the direct numerical solution of the exact integral equation, and find complete agreement.
Topics & Concepts
Non-perturbativeSigmaSeries (stratigraphy)PhysicsField (mathematics)Energy (signal processing)Order (exchange)Mathematical physicsTheoretical physicsQuantum electrodynamicsStatistical physicsQuantum mechanicsMathematicsPure mathematicsEconomicsFinancePaleontologyBiologyBlack Holes and Theoretical PhysicsQuantum Chromodynamics and Particle InteractionsNonlinear Waves and Solitons