Analytic resurgence in the O(4) model

Abstract

We study the perturbative expansion of the ground state energy in the presence of an external field coupled to a conserved charge in the integrable two-dimensional O$(4)$ nonlinear sigma model. By solving Volin's algebraic equations for the perturbative coefficients we study the large order asymptotic behaviour of the perturbative series analytically. We confirm the previously numerically found leading behaviour and study the nearest singularities of the Borel transformed series and the associated alien derivatives. We find a 'resurgence' behaviour: the leading alien derivatives can be expressed in terms of the original perturbative series. A simplified 'toy' model is also considered: here the perturbative series can be found in a closed form and the resurgence properties are very similar to that found in the real problem.

35 pages, LaTeX, no figures

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• Resurgence in the O(4) sigma model
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• Asymptotics in an Asymptotic CFT
• All-order Resurgence from Complexified Path Integral in a Quantum Mechanical System with Integrability
• Resurgence in the Scalar Quantum Electrodynamics Euler-Heisenberg Lagrangian
• Asymptotics in the bi-Yang-Baxter Sigma Model