Resurgence and Lefschetz thimble in three-dimensional supersymmetric Chern–Simons matter theories

Fujimori, Toshiaki (Department of Physics, and Research and Education Center for Natural Sciences, Keio University, 4-1-1 Hiyoshi, Yokohama, Kanagawa 223-8521, Japan) ; Honda, Masazumi (Department of Particle Physics, Weizmann Institute of Science, Rehovot 7610001, Israel) ; Kamata, Syo (Department of Physics, North Carolina State University, Raleigh, NC 27695, USA) ; Misumi, Tatsuhiro (Department of Physics, and Research and Education Center for Natural Sciences, Keio University, 4-1-1 Hiyoshi, Yokohama, Kanagawa 223-8521, Japan) (Department of Mathematical Science, Akita University, Akita 010-8502, Japan) (iTHEMS, RIKEN, 2-1 Hirasawa, Wako, Saitama 351-0198, Japan) ; Sakai, Norisuke (Department of Physics, and Research and Education Center for Natural Sciences, Keio University, 4-1-1 Hiyoshi, Yokohama, Kanagawa 223-8521, Japan) (iTHEMS, RIKEN, 2-1 Hirasawa, Wako, Saitama 351-0198, Japan)

23 December 2018

Abstract: We study a certain class of supersymmetric (SUSY) observables in three-dimensional SUSY Chern–Simons (CS) matter theories and investigate how their exact results are related to the perturbative series with respect to coupling constants given by inverse CS levels. We show that the observables have non-trivial resurgent structures by expressing the exact results as a full transseries consisting of perturbative and non-perturbative parts. As real mass parameters are varied, we encounter Stokes phenomena at an infinite number of points, where the perturbative series becomes non-Borel-summable due to singularities on the positive real axis of the Borel plane. We also investigate the Stokes phenomena when the phase of the coupling constant is varied. For these cases, we find that the Borel ambiguities in the perturbative sector are canceled by those in non-perturbative sectors and end up with an unambiguous result which agrees with the exact result even on the Stokes lines. We also decompose the Coulomb branch localization formula, which is an integral representation for the exact results, into Lefschetz thimble contributions and study how they are related to the resurgent transseries. We interpret the non-perturbative effects appearing in the transseries as contributions of complexified SUSY solutions which formally satisfy the SUSY conditions but are not on the original path integral contour.


Published in: PTEP 2018 (2018) 123B03
Published by: Oxford University Press/Physical Society of Japan
DOI: 10.1093/ptep/pty118
arXiv: 1805.12137
License: CC-BY-3.0



Back to search

Fulltext:
Download fulltextPDF Download fulltextXML Download fulltextPDF (PDFA)