Abstract
Localization methods have recently led to a plethora of new exact results in supersymmetric gauge theories, as certain observables may be computed in terms of matrix integrals. These can then be evaluated by making use of standard large N techniques, or else via perturbative expansions in the gauge coupling. Either approximation often leads to observables given in terms of asymptotic series, which need to be properly defined in order to obtain nonperturbative results. At the same time, resurgent analysis has recently been successfully applied to several problems, e.g., in quantum, field and string theories, precisely to overcome this issue and construct nonperturbative answers out of asymptotic perturbative expansions. The present work uses exact results from supersymmetric localization to address the resurgent structure of the free energy and partition function of Chern-Simons and ABJM gauge theories in three dimensions, and of \( \mathcal{N}=2 \) supersymmetric Yang-Mills theories in four dimensions. For each case, the complete structure of Borel singularities is exactly determined, and the relation of these singularities with the large-order behavior of (multi-instanton) perturbative expansions is made fully precise.
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ArXiv ePrint: 1410.5834
From October 2014: Institute of Physics, Jagiellonian University, ul. Lojasiewicza 11, 30-348 Kraków, Poland. (Inês Aniceto)
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Aniceto, I., Russo, J.G. & Schiappa, R. Resurgent analysis of localizable observables in supersymmetric gauge theories. J. High Energ. Phys. 2015, 172 (2015). https://doi.org/10.1007/JHEP03(2015)172
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DOI: https://doi.org/10.1007/JHEP03(2015)172