Borel Summability of Perturbative Series in 4D N=2 and 5D N=1 Supersymmetric Theories

Masazumi Honda
Phys. Rev. Lett. 116, 211601 – Published 25 May 2016

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 the zero-instanton sector are Borel summable for various observables. Our result for the 4D 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 an arbitrary number of instanton sectors are Borel summable for a wide class of theories. It turns out that exact results can be obtained by summing over the Borel resummations with every instanton number.

  • Received 29 March 2016

DOI:https://doi.org/10.1103/PhysRevLett.116.211601

© 2016 American Physical Society

Physics Subject Headings (PhySH)

Particles & Fields

Authors & Affiliations

Masazumi Honda*

  • Department of Particle Physics, Weizmann Institute of Science, Rehovot 7610001, Israel

  • *masazumi.honda@weizmann.ac.il

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Issue

Vol. 116, Iss. 21 — 27 May 2016

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