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

Abstract: Is it possible to derive non-perturbative contributions in a quantum field theory knowing only the perturbative coefficients? We answer this question affirmatively based on the careful analysis of the integrable two dimensional O(4) sigma model. We investigate its ground state energy in a magnetic field, for which integrability provides an exact linear integral equation. By cleverly expanding this equation we could calculate a large number of very precise, factorially growing perturbative coefficients. By investigating their asymptotical behaviour on the Borel plane we managed to reveal a nice resurgence structure leading to the first few exponentially suppressed non-perturbative terms of the ambiguity free trans-series. We checked our results against the direct numerical solution of the exact integral equation and find complete agreement. (based on 2011.12254 and 2011.09897)

condensed mattergeneral relativity and quantum cosmologyHEP - theorymathematical physicsexactly solvable and integrable systems

Audience: researchers in the topic

( paper )

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SEU Yau Center Theoretical Physics Seminars 2021

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