Resurgence and Lefschetz thimble in three-dimensional $\mathcal{N}=2$ supersymmetric Chern?Simons matter theories
Resurgence and Lefschetz thimble in three-dimensional $\mathcal{N}=2$ supersymmetric Chern?Simons matter theories
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三维 $mathcal{N}=2$ 超对称 Chern?Simons 物质理论中的中兴和 Lefschetz 顶针
DOI：
10.1093/ptep/pty118
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发表时间：
2018
影响因子：
3.5
通讯作者：
Sakai Norisuke
中科院分区：
文献类型：
--
作者：
Fujimori Toshiaki;Honda Masazumi;Kamata Syo;Misumi Tatsuhiro;Sakai Norisuke
本文研究了三维超对称（SUSY）Chern-Simons（CS）物质理论中的一类超对称（SUSY）观测量，并研究了它们的精确结果与由反CS能级给出的耦合常数的微扰级数之间的关系.我们表明，观测值有非平凡的复苏结构，通过表达的确切结果作为一个完整的transseries组成的微扰和非微扰部分。由于真实的质量参数是变化的，我们遇到斯托克斯现象在无穷多个点，在那里的微扰系列成为非波莱尔求和由于奇异的正真实的轴上的波莱尔平面。我们还研究了当耦合常数的相位变化时的斯托克斯现象。对于这些情况下，我们发现，在微扰部门的Borel模糊性被取消的非微扰部门，并最终与确切的结果，即使在斯托克斯线同意一个明确的结果。我们还分解的库仑分支本地化公式，这是一个完整的表示的确切结果，到Lefschetz顶针的贡献，并研究它们是如何相关的复苏transseries。我们解释的非微扰效应出现在transseries的贡献复杂的超对称性解决方案，正式满足超对称性条件，但不是在原来的路径积分轮廓。
We study a certain class of supersymmetric (SUSY) observables in three-dimensionalSUSY 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.