The full analytic trans-series in integrable field theories

Abstract

We analyze a family of generalized energy densities in integrable quantum field theories in the presence of an external field coupled to a conserved charge. By using the Wiener-Hopf technique to solve the linear thermodynamic Bethe ansatz equations we derive the full analytic trans-series for these observables in terms of a perturbatively defined basis. We show how to calculate these basis elements to high orders analytically and reveal their complete resurgence structure. We demonstrate that the physical value of the generalized energy densities is obtained by the median resummation of their ambiguity-free trans-series.

arXiv comment13 pages, 1 figure, v2: minor additions

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• Exact instanton transseries for quantum mechanics
• Condensates, crystals, and renormalons in the Gross-Neveu model at finite density
• Trans-series from condensates
• Asymptotics in the bi-Yang-Baxter Sigma Model