This project is devoted to the study of elementary particle physics, including its connections to other areas of study ranging from astrophysics and cosmology to condensed matter physics and geometry. The project will partly support the research of the principal investigator, a senior visitor, and a substantial group of postdoctoral fellows who are working on these topics. Current and planned research of this group covers a very wide range of topics, including the connections between gauge theory (the modern language of elementary particle physics) and geometry; the possibilities for supersymmetric models of particle physics that might be relevant at accelerator energies; new methods of computing and studying the scattering amplitudes of elementary particles; new experimental hints of cosmic dark matter; new relations among old and new quantum field theories in different dimensions; neutrino physics; and more.
The broader impacts of this proposal include the training of a large number of young postdoctoral researchers. For many years, the Institute for Advanced Study has provided an ideal ``training ground'' for young postdocs to work with the best of their peers, and gather critical research experience. Ultimately, IAS postdocs help populate the most active teaching and research institutions in the country, serving in turn as mentors and teachers of students in the physical and biological sciences.
This project supported research by a large group of postdoctoral fellows -- members of the Institute for Advanced Study -- and senior visitors, and also the principal investigator, Edward Witten. The research concerned a broad range of problems in quantum field theory, string theory, and particle physics, including relations with other areas of science, notably astrophysics, condensed matter physics, and mathematics. Specific topics in which notable contributions were made by researchers on this grant include new understanding of perturbative scattering amplitudes in gauge theory, which are important in hadron collider physics; entanglement of many-body quantum mechanical wavefunctions; quantum mechanical behavior of gauge theories, especially in the supersymmetric case, and with many links to string theory; and new probes of the dark matter of the Milky Way galaxy. These are all very active areas of research worldwide and research supported by this grant has been in the forefront of developments in all of these areas. The research of the principal investigator during this grant period dealt primarily with two topics. One topic was the development of a new approach to the mathematics of knots using quantum physics. This work involved bringing to bear some of the modern ideas about ``dualities'' in quantum physics along with an essentially new viewpoint on the Feynman path integral. The second topic was a reconsideration of the fundamentals of superstring perturbation theory, which is the technique to compute quantum behavior of string theory when the quantum mechanical effects are small. Here the main idea was to base everything on supergeometry rather than ordinary geometry. The output of this work was to formulate superstring perturbation theory in a significantly more precise way than was achieved previously.
