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

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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.