This award funds the research activities of Professor Yong-Shi Wu at the University of Utah.
For the past two decades, string theory has been one of the most intensely investigated areas of theoretical high-energy physics. This is true chiefly because string theory offers what is currently the most successful method of unifying gravity with the other fundamental forces (strong, weak, and electromagnetic). Results from string theory have also spilled over into many other branches of physics, leading to improved understanding of gauge theories, condensed-matter physics, and heavy-ion physics. String theory has also led to powerful new insights in mathematics. In this project, Professor Wu aims to study algebraic and geometric structures in quantum field theory and string theory, which he envisions to provide a theoretical framework for accounting for all fundamental interactions in particle physics. The PI plans to focus, specifically, on the possibility of new states of matter, with the idea that better understanding new states of matter should help us better understand the origin of our Cosmos and its past (particularly early) history. This work will also have important connections to condensed-matter physics.
This project is also envisioned to have several broader impacts. Graduate students and postdocs will be supported and trained to be future professionals. The PI will present seminars and thereby prompt scientific exchanges of ideas. Scholarly review articles and articles describing research to non-specialist audiences will be written to convey recent developments to colleagues in the physics community and to the general public. The PI is also writing a new textbook, "Physics and Geometry", and developing new classroom instructional materials.
This project was a continuing one in High Energy Theory and Particle Physics. It supported theoretical research of fundamental laws in elementary particle physics (including quantum field and string theory), which are deeply relevant to understanding the origin, composition and evolution of our universe. Applications of quantum field theory to quantum dynamics of many-body systems are leading to and will further lead to better understanding of new states of matter, which may have a great impact on understanding the physical laws emergent at the hitherto thought-to-be fundamental level. So in this project, the PI proposed to study quantum field theories both in particle physics (including those relevant to string theory) and in condensed matter many-body physics. On the one hand, this project investigated algebraic and geometric aspects or structures in quantum field theory and string theory, which will provide a theoretical framework for accounting for all fundamental interactions in particle physics. Particular attention is paid to the unification of quantum theory and general relativity, two cornerstones of the 20th century physics. This unification requires modification of the spacetime/gravity theory proposed by Einstein. A promising candidate for this modification and unification is string theory and its extension, the so-called M-theory. The latter is a conjectured theory in 11 dimensional spacetime, with the so-called M-membranes as fundamental objects, of which all stuff in our universe is made. This theory unifies five known distinct string theories as its special cases and, therefore, is thought to be more fundamental than string theory. This project studied the effective field theories that describe the behavior of various configurations of a collection of M-membranes. The outcomes of this study enlarged the scope of the effective theories known in the literature, so that the dynamics of more possible M-membrane configurations is within our reach. Also this study discoveries a mathematical structure, the so-called N=4 3-algebra, underlying a large class of effective theories for M-membranes. This will help advance our understanding of M-membrane dynamics. On the other hand, better understanding of new states of matter should provide a new window into the deep secrets of our Cosmos. For we know that our Cosmos is a many-body system and its state has undergone dramatic changes in its early past, similar to ice-water-vapor transitions in daily life. This project studied a particular class of newly recognized many-body states in condensed matter systems, called topological states of matter, which are described by a particular class of topological quantum field theory. The PI has spent thirty years working on the relevant subfields and problems. This project studied a large class of exactly solvable discrete models, which describe the topological matter in two-dimensional (cylindrical or toroidal) systems and become topological quantum field theories at large scales. New methods were developed to obtain exact solutions for both the lowest-energy states and the excitations above them. From the solutions, explicit and pictorial understanding is acquired for the underlying physics mechanisms responsible for many exotic phenomena happening in topological matter. Numerical computation is also done in more realistic lattice models, for materials such as ultra-thin Bismuth films and an organic metallic framework we proposed, demonstrated new ways/possibilities to implement topological states of matter in the real world systems. The analytic results may promote relevant mathematics in topology and algorithms in quantum computation, while the numerical results may inspire advances in making devices in topological quantum computation and quantum information processing. In addition, this project has had the following broader impacts: several graduate students and postdocs have been supported and trained to become professional scientists. The PI attended various workshops and symposia, domestic or international, presenting seminars and prompting scientific exchanges of ideas. Scholarly review articles and those describing research to non-specialist audiences were written to convey recent excitements in the frontiers to colleagues in physics community and to rally supports to basic research from the general public. Support to ongoing collaborations of the PI with scientists from other countries has brought top students, postdocs, teachers etc, including those from under-served demographic groups and those from Asia Pacific and Latin America, to Utah, and promoted international exchange of scientists and recruitment of new young talents into the work force in the US. The PI is writing a new textbook on "Physics and Geometry", developing new classroom instructional materials and updating the curriculum of graduate students in theoretical physics. Moreover, the project on devising new quantum field or string theoretical models for the very early Universe in extreme conditions could lead to forging new links to other scientific disciplines, such as theoretical and experimental astrophysics and cosmology. And the outcomes of this project on applying quantum field theory to new states of condensed matter could be relevant to topological quantum computation, an emerging interdisciplinary field in science, which needs insights from mathematics, physics and computer science to make progress.
