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Borel summability of perturbative series in 4d N=2 and 5d N=1 theories
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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.
Forward citations
Cited by 2 Pith papers
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Instantons from Blow-up
The instanton partition function of many 4d N=2 and 5d N=1 gauge theories is fully determined by the perturbative part via generalized Nakajima-Yoshioka blowup equations.
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Extremal Correlators and Random Matrix Theory
Extremal correlators in rank-1 N=2 SCFTs are governed at large charge by a Wishart-Laguerre random matrix model, whose 't Hooft expansion reproduces effective field theory and predicts strong-coupling nonperturbative ...
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