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arXiv 1604.08653hep-thcond-mat.str-elmath-phmath.MP
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3d N=2 Chern-Simons物质理论中微扰级数的求和

How to resum perturbative series in 3d N=2 Chern-Simons matter theories

Masazumi Honda

备注：
8 pages, 1 figure; v3:introduction improved
发表信息：
Phys. Rev. D 94, 025039 (2016)
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摘要：

在arXiv：1603.06207的基础上，我们研究了一般三维$\mathcal{N}=2$超对称Chern-Simons物质理论中的微扰级数，该理论具有$U(1)_R$对称性，由反Chern-Simons能级的幂级数展开给出.我们发现，对于各种观测量，微扰级数沿正实轴通常是非Borel可和的。另外，我们证明了微扰级数总是Borel可和沿负（正）虚轴的正（负）Chern-Simons水平。结果表明，沿此方向的Borel插值与精确结果相同，因而是微扰级数插值的正确方法。

英文摘要：

Continuing the work arXiv:1603.06207, we study perturbative series in general 3d $\mathcal{N}=2$ supersymmetric Chern-Simons matter theory with $U(1)_R$ symmetry, which is given by a power series expansion of inverse Chern-Simons levels. We find that the perturbative series are usually non-Borel summable along positive real axis for various observables. Alternatively we prove that the perturbative series are always Borel summable along negative (positive) imaginary axis for positive (negative) Chern-Simons levels. It turns out that the Borel resummations along this direction are the same as exact results and therefore correct ways of resumming the perturbative series.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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