From perturbative to non-perturbative in the O(4) sigma model

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.

5 pages, 3 figures. v2 adds some references, one more term d_3, v3: some explanations are clarified, document is restructured, 11 pages now

References in corpus (5)

• Nonperturbative effects and nonperturbative definitions in matrix models and topological strings
• Non-perturbative Contributions from Complexified Solutions in $\mathbb{C}{P}^{N-1}$ Models
• Scaling function in AdS/CFT from the O(6) sigma model
• Resurgence in the O(4) sigma model
• Conformal mapping of the Borel plane: going beyond perturbative QCD

Cited by in corpus (14)

• New renormalons from analytic trans-series
• Testing the Bethe ansatz with large N renormalons
• The full analytic trans-series in integrable field theories
• Analytic resurgence in the O(4) model
• Instanton effects vs resurgence in the $O(3)$ sigma model
• Instantons, renormalons and the theta angle in integrable sigma models
• Resurgence in Lorentzian quantum cosmology: No-boundary saddles and resummation of quantum gravity corrections around tunneling saddle points
• Quantum phase transition and Resurgence: Lessons from 3d $\mathcal{N}=4$ SQED
• Running coupling and non-perturbative corrections for O$(N)$ free energy and for disk capacitor
• Asymptotics in an Asymptotic CFT
• 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 and $1/N$ Expansion in Integrable Field Theories
• Asymptotics in the bi-Yang-Baxter Sigma Model