Authors: Gökçe Basar Gerald V Dunne
Publish Date: 2015/02/25
Volume: 2015, Issue: 2, Pages: 160-
Abstract
The NekrasovShatashvili limit for the lowenergy behavior of mathcalN=2 and mathcalN=2 supersymmetric SU2 gauge theories is encoded in the spectrum of the Mathieu and Lamé equations respectively This correspondence is usually expressed via an allorders BohrSommerfeld relation but this neglects nonperturbative effects the nature of which is very different in the electric magnetic and dyonic regions In the gauge theory dyonic region the spectral expansions are divergent and indeed are not Borelsummable so they are more properly described by resurgent transseries in which perturbative and nonperturbative effects are deeply entwined In the gauge theory electric region the spectral expansions are convergent but nevertheless there are nonperturbative effects due to poles in the expansion coefficients and which we associate with worldline instantons This provides a concrete analog of a phenomenon found recently by Drukker Mariño and Putrov in the large N expansion of the ABJM matrix model in which nonperturbative effects are related to complex spacetime instantons In this paper we study how these very different regimes arise from an exact WKB analysis and join smoothly through the magnetic region This approach also leads to a simple proof of a resurgence relation found recently by Dunne and Ünsal showing that for these spectral systems all nonperturbative effects are subtly encoded in perturbation theory and identifies this with the PicardFuchs equation for the quantized elliptic curveThis article is published under an open access license Please check the Copyright Information section for details of this license and what reuse is permitted If your intended use exceeds what is permitted by the license or if you are unable to locate the licence and reuse information please contact the Rights and Permissions team
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