Quantum Hall Effect(QHE) is a remarkable achievement in condensed matter physics and is profoundly connected to other fields in physics and fundamental mathematics. A major development in this field in recent years is the theory of higher Dimensional Quantum Hall Systems(HDQHS). Accumulated evidence suggests deep connections between the world of HDQHS and the world of particle physics and string theory. The proposed research here aims to explore the physics related to HDQHS. A series of specific projects will be initiated to study the mathematical structures and the physical properties of HDQHS, to explore the connections between HDQHS and particle physics/string theory, and to develop realistic models of solid state systems that possess HDQHS physics. The research is motivated by the beauty of the fundamental unity between HDQHS and unique mathematical topological structures, the physical properties of HDQHS and the associated fundamental physics in QCD and string theory. Intellectual merit: (1) The research will make clear the rich and important physical properties of HDQHS and provide a conceptual framework for studying fundamental mechanisms in physics. (2)The research will shed new light on a number of fundamental problems of theoretical physics, such as new phases in higher dimension, gauge anomaly at orbifold geometry and Yang Mills theory of gluons in 3+1 dimensions, and introduce new approaches to test modern ideas in particle physics. (3) The proposed research will highlight the interplay of condensed matter physics and particle physics and pioneer the creation of possible new interdisciplinary research frontiers. Broader impact: This project is an exceptional example to show students the fundamental unity of the physics world despite the apparent diversity in modern physics research. Further more, it provides unique opportunities to educate students in all aspects of modern theoretical physics and to stimulate among a new generation of future physicists an interest in and an appreciation for fundamental research that cuts across disciplinary boundaries. Past research in this field has attracted considerable attention from the news media and the general public. The proposed project will continue to bring to the public exciting advances in the forefront of modern physics research.
