论文标题
关于雷诺马龙在综合理论中的复兴
On the resurgence of renormalons in integrable theories
论文作者
论文摘要
在本论文中，我们在复兴框架下探索了可融合模型中雷诺马龙的物理学。在第一部分中，我们回顾了一些关于重新恢复，集成性和肾结足的背景，包括对大型N肾小球和环图的讨论。在第二部分中，我们从Bethe Ansatz积分方程开始，并在多个模型中获得自由能的精确跨系列。这些跨系列包括非扰动效应，这些效应对应于肾结石平面的意外位置。我们以数值为单位测试跨系列。在拓扑角度，我们还研究了这些跨系列会发生什么。在第三部分中，我们使用在非忠实理论中应用复兴技术。我们发现系统的能量间隙与骨平面中的奇异点位置之间的关系。通过研究环图的渐近行为，我们确定了与肾甲龙的关系。
In this thesis we explore the physics of renormalons in integrable models under the framework of resurgence. In the first part, we review some background on resurgence, integrability and renormalons, including a discussion of large N renormalons and ring diagrams. In the second part, we start from the Bethe ansatz integral equations and obtain exact trans-series for the free energy in multiple models. These trans-series include non-perturbative effects which correspond to renormalons at unexpected positions in the Borel plane. We test the trans-series numerically and at large N. We also study what happens to these trans-series under a topological angle. In the third part, we use apply the techniques of resurgence in non-relativistic theories. We find a relation between the energy gap of the system and the positions of singularities in the Borel plane. By studying the asymptotic behaviour of ring diagrams, we identify this relation with renormalons.
