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arXiv · 1603.06207

Borel summability of perturbative series in 4d N=2 and 5d N=1 theories

Masazumi Honda
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Abstract

We study weak coupling perturbative series in 4d N=2 and 5d N=1 supersymmetric gauge theories with Lagrangians. We prove that the perturbative series of these theories in zero instanton sector are Borel summable for various observables. Our result for 4d $\mathcal{N}=2$ case supports an expectation from a recent proposal on a semiclassical realization of infrared renormalons in QCD-like theories, where the semiclassical solution does not exist in N=2 theories and the perturbative series are unambiguous, namely Borel summable. We also prove that the perturbative series in arbitrary number of instanton sector are Borel summable for a wide class of theories. It turns out that exact results can be obtained by summing over the Borel resummations in each number of instanton sector.

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Masazumi Honda. 2016-05-07. Borel summability of perturbative series in 4d N=2 and 5d N=1 theories. https://doi.org/10.1103/physrevlett.116.211601

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