Strong interactions beyond the Standard Model: Supersymmetry on the lattice, dualities, and confinement

现代粒子物理学的基本开放问题需要新的分析概念和方法，同时必须通过数值方法来确认和扩展。最终的目标不仅是与数值和实验数据的一致性，而是对基本理论和基本机制的理解。这个项目是基于数值计算和理论概念之间的相互作用。粒子物理学的现有知识总结在标准模型中。在这个描述中揭示的开放问题是对暗物质的解释，标准模型中引力的包含，对量子色动力学（QCD）基本机制的理解，以及标准模型的概念缺陷。天文观测提供了合理的证据，证明宇宙中有很大一部分暗物质是当前理论无法解释的。到目前为止，还没有找到一个一致的量子引力理论，但斯汀理论被认为是一个有希望的候选者。夸克在核子中的强相互作用导致了时空格子上的数值模拟所显示的禁闭，但到目前为止，它还无法获得解析理解。在这个项目中，我计划研究超越标准模型的强相互作用超对称规范理论，为解决这些基本问题提供新的概念和方法。它们与标准模型的扩展有关，并为理解强相互作用和量子引力提供了理论方法。在这个项目中考虑的超对称规范理论是基于类似QCD的强动力学。因此，它们一般只能通过数值方法来获得。由于扩展的对称性，显着的额外的分析见解是可能的，应该验证和扩展的数值方法。量子引力公式化的基本问题和对弦理论的基本理解与规范-引力对偶的超对称规范理论有关。该项目的第一个目标是对超对称规范理论的数值模拟方法进行实质性的推广。三个不同的主题将解决这些方法：标准模型的超对称扩展的一致制定，基于半经典描述的约束机制的理解，以及基于超对称规范理论动力学的弦理论的调查。

The fundamental open problems of modern particle physics require new analytical concepts and approaches that must at the same time be confirmed and extended by numerical methods. The final goal is not only an agreement with numerical and experimental data, but rather an understanding of the fundamental theory and the basic mechanisms. This project is based on this interplay between numerical computations and theoretical concepts.The current knowledge of particle physics is summarized in the Standard Model. The open problems revealed in this description are the explanation for Dark Matter, the inclusion of gravity in the Standard Model, the understanding of basic mechanisms of quantum chromodynamics (QCD), and conceptional shortcomings of the Standard Model. Astronomical observations provide reasonable evidence for a large proportion of Dark Matter in the universe that is not explained by the current theory. A consistent theory for quantum gravity has so far not been found, but sting theory is considered to be a promising candidate. The strong interaction of quarks in nucleons leads to confinement as shown by numerical simulations on a space-time lattice, but it is so far not accessible for an analytical understanding.In this project I plan to investigate strongly interacting supersymmetric gauge theories beyond the Standard Model, that provide new concepts and approaches towards a solution of these fundamental problems. They are related to extensions of the Standard Model and they provide theoretical approaches for an understanding of strong interactions and quantum gravity. The supersymmetric gauge theories considered in this project are based on a similar strong dynamics as QCD. Therefore they are in general only accessible by numerical methods. Due to the extended symmetry, remarkable additional analytical insights are possible, that should be verified and extended by numerical methods. The fundamental problem of the formulation of quantum gravity and a basic understanding of string theory is related to supersymmetric gauge theories by gauge-gravity dualities.The first objective of the project is a substantial generalization of the methods for the numerical simulation of supersymmetric gauge theories. Three different topics will be addressed with these methods: the consistent formulation of supersymmetric extensions of the Standard Model, the understanding of the confinement mechanism based on a semi-classical description, and the investigation of string theory based on the dynamics of supersymmetric gauge theories.