arXiv 2006.091132020-06hep-latcs.LGhep-th

拓扑缺陷和机器学习的限制：紧凑电动力学中的单极子的情况

Topological defects and confinement with machine learning: the case of monopoles in compact electrodynamics

Institut Denis Poisson CNRS/UMR 7013（丹尼斯·泊松研究所（法国国家科学研究中心/7013联合研究单位））；Université de Tours（图尔大学）；Pacific Quantum Center（太平洋量子中心）；Far Eastern Federal University（远东联邦大学）；Dipartimento di Fisica, Universitá di Torino（都灵大学物理系）；INFN Sezione di Torino（意大利国家核物理研究所都灵分所）；Arnold-Regge Center（阿诺德-雷格中心）

M. N. Chernodub, Harold Erbin, V. A. Goy, A. V. Molochkov

备注：: 15 pages, 36 figures; minor revisions, published version
发表信息：: Phys. Rev. D 102, 054501 (2020)
DOI：: 10.1103/PhysRevD.102.054501

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摘要：

我们研究了机器学习技术在量子场论中识别拓扑对象动力学的优势。我们考虑三维时空中的紧致U（1）规范理论，作为展示由单极子产生的禁闭和质量间隙现象的理论的最简单的例子。我们训练一个神经网络与生成的一组配置，以区分约束和解除约束阶段，从它是可能的，以确定解除约束过渡点，并预测几个可观的。该模型使用监督学习方法，并将三维图像（全息图）的三维配置。我们表明，该模型可以准确地确定转变温度，这取决于在算法中实现的标准。更重要的是，我们训练神经网络的配置从一个单一的晶格尺寸之前，从其他晶格尺寸的配置，从可靠的估计得到的临界温度的预测。

英文摘要：

We investigate the advantages of machine learning techniques to recognize the dynamics of topological objects in quantum field theories. We consider the compact U(1) gauge theory in three spacetime dimensions as the simplest example of a theory that exhibits confinement and mass gap phenomena generated by monopoles. We train a neural network with a generated set of monopole configurations to distinguish between confinement and deconfinement phases, from which it is possible to determine the deconfinement transition point and to predict several observables. The model uses a supervised learning approach and treats the monopole configurations as three-dimensional images (holograms). We show that the model can determine the transition temperature with accuracy, which depends on the criteria implemented in the algorithm. More importantly, we train the neural network with configurations from a single lattice size before making predictions for configurations from other lattice sizes, from which a reliable estimation of the critical temperatures are obtained.

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