Nonperturbative physics in sigma models

二维sigma模型是一类重要的强耦合系统，具有渐近自由度、动态产生的质量隙等重要性质，与量子色动力学有着密切的联系。最近，两个非常有趣的非微扰效应已在这些系统中进行了研究：微扰重正马龙奇性的分数瞬子贡献的取消和产生一个非零的电荷密度的化学势通过制定在对偶变量。这两个主题都将在本项目中进行，主要使用网格技术。时空格点上的离散化是非微扰物理学中为数不多的从头算方法之一。该项目的目的是在数值上检查这些模型中的renormalon猜想，并进一步开发结构问题的对偶变量和非零密度及以上的特定模拟。

Two-dimensional sigma models are prominent strongly coupled systems sharing asymptotic freedom, a dynamically generated mass-gap and other important properties with Quantum chromodynamics. Recently, two very interesting nonperturbative effects have been studied in these systems: the cancellation of perturbative renormalon singularities by fractional instanton contributions and the generation of a nonzero charge density by a chemical potential through a formulation in terms of dual variables. Both topics shall be advanced in this project, mainly using lattice techniques. Discretisations on space-time lattices are one of the very few ab initio approaches to nonperturbative physics. The project aims at checking the renormalon conjecture in these models numerically as well as further developing dual variables for structural questions and specific simulations at nonzero density and beyond.