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arXiv 2108.02647hep-thhep-lathep-phmath-phmath.MP
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可积场论中的回复与$1/N$展开

Resurgence and $1/N$ Expansion in Integrable Field Theories

Lorenzo Di Pietro, Marcos Mariño, Giacomo Sberveglieri, Marco Serone

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59 pages, 5 figures
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摘要：

在具有重整化子的理论中，微扰级数即使在限制到$1/N$中的给定阶之后也是阶乘发散的，这使得$1/N$展开成为复活理论的自然试验场。我们详细研究了在各种可积场论与重整化子的复苏性质和$1/N$展开之间的相互作用。我们专注于自由能的存在下，化学势耦合到一个保守的电荷，这可以准确地计算与热力学贝特分析（TBA）。在一些示例中，类似于对非线性西格玛模型中的自由能的第一$1/N$校正，$1/N$展开中的项可以根据耦合常数中的重新出现的反式级数来完全解码。在主手征领域，我们找到了一个新的，明确的解决方案，大$N$自由能，可以被写为一个具有无限多个，解析计算IR重整化修正的反系列的中位数remmation。然而，在其他例子中，如Gross-Neveu模型，在$1/N$展开中的每一项包括非微扰修正，其不能通过相应的微扰序列的复苏分析来预测。我们还研究了$1/N$中级数的性质。在Gross-Neveu模型中，这是收敛的，我们解析地继续系列超出其收敛半径，并显示如何继续与已知的对偶与正弦戈登理论相匹配。

英文摘要：

In theories with renormalons the perturbative series is factorially divergent even after restricting to a given order in $1/N$, making the $1/N$ expansion a natural testing ground for the theory of resurgence. We study in detail the interplay between resurgent properties and the $1/N$ expansion in various integrable field theories with renormalons. We focus on the free energy in the presence of a chemical potential coupled to a conserved charge, which can be computed exactly with the thermodynamic Bethe ansatz (TBA). In some examples, like the first $1/N$ correction to the free energy in the non-linear sigma model, the terms in the $1/N$ expansion can be fully decoded in terms of a resurgent trans-series in the coupling constant. In the principal chiral field we find a new, explicit solution for the large $N$ free energy which can be written as the median resummation of a trans-series with infinitely many, analytically computable IR renormalon corrections. However, in other examples, like the Gross-Neveu model, each term in the $1/N$ expansion includes non-perturbative corrections which can not be predicted by a resurgent analysis of the corresponding perturbative series. We also study the properties of the series in $1/N$. In the Gross-Neveu model, where this is convergent, we analytically continue the series beyond its radius of convergence and show how the continuation matches with known dualities with sine-Gordon theories.

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