Universal renormalons in principal chiral models
Universal renormalons in principal chiral models
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DOI：
10.1103/physrevd.101.034513
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发表时间：
2020-02-18
影响因子：
5
通讯作者：
Puhr, Matthias
中科院分区：
文献类型：
--
作者：
Bruckmann, Falk;Puhr, Matthias
在许多物理系统中，微扰展开式产生的“只有”渐近级数甚至不是Borel可恢复的。有趣的是，相应的模糊性指向非微扰物理学。我们首次在二维sigma模型中数值验证了这一重整机制，该模型与四维规范理论一样，是渐近自由的，并通过维度嬗变产生强尺度。我们通过随机量子化的数值版本扰动扩展能量。与第一阶能量系数相比，高阶系数与模型的秩无关。从技术上讲，它们需要对有限体积效应和离散模型的连续体极限进行复杂的分析。虽然单个系数不是因式增长，而是强烈减少，但连续系数的比值明显服从正则化渐近。
Perturbative expansions in many physical systems yield "only" asymptotic series which are not even Borel resummable. Interestingly, the corresponding ambiguities point to nonperturbativc physics. We numerically verify this renormalon mechanism for the first time in two-dimensional sigma models, that, like four-dimensional gauge theories, are asymptotically free and generate a strong scale through dimensional transmutation. We perturbatively expand the energy through a numerical version of stochastic quantization. In contrast to the first energy coefficients, the high-order coefficients arc independent on the rank of the model. Technically, they require a sophisticated analysis of finite volume effects and the continuum limit of the discretized model. Although the individual coefficients do not grow factorially (yet), but rather decrease strongly, the ratios of consecutive coefficients clearly obey the renormalon asymptotics.