As explained in Weinberg's The Quantum Theory of Fields, Volume 2, Chapter 20.7 Renormalons, instantons are a known source of poles in the Borel transform of the perturbative series. These poles are on the negative real axis, and the series remains Borel-summable as long as the coupling constant is not too large.
However, instantons are objects in the Euclidean version of QFT. What's the significance of the above Borel resummation in the Minkowski theory?
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