This award funds the research activities of Professor Lara B. Anderson at Virginia Tech.
Fundamental particle physics is at a critical moment in its development. New studies at the Large Hadron Collider, the Planck satellite and other experiments will give new information on possible physics beyond the Standard Model. This project is motivated by this goal. It is focused on string theory, which hopes to unify gravity with the other fundamental forces. String theory is only manifest at very high energy scales. To connect with experiment, the project concentrates on the development of "string phenomenology" - the aspect of string theory that attempts to bridge the gap between the high-energy, extra-dimensional formalism of string theory, and the low-energy, four-dimensional world of particles and forces. Despite the importance of string theory as the only known consistent quantum theory of gravity and its enormous power and flexibility for so-called "top down" model building in high energy physics, it is only recently that explicit low-energy limits of string theory have started to be developed to a level that makes serious interdisciplinary contact between string and particle phenomenology possible. Within string theory, the roles of physics and mathematics are intrinsically intertwined, and progress in string phenomenology requires cutting edge tools in modern mathematics. This project involves three of the primary approaches to particle phenomenology in string theory and interlinked approaches to string theory, algebraic geometry and high-speed mathematical computing. Now is the time to attempt to answer the question: can string theory give a description of the real world? And at last, with interdisciplinary mathematical and physical approaches and expanding computational power, string phenomenology is capable of doing just that. By exploring these new geometries, it may be possible to find a view of string theory that looks profoundly similar to the world we observe.
In heterotic string theory, the PI will generate a database of hundreds of billions of heterotic models (composed of Calabi-Yau 3-folds and vector bundles defined over them) and the analytic and algorithmic tools necessary to completely analyze the geometries and compute their local and topological data. The PI will also use new approaches in computational algebraic geometry to address long-standing phenomenological challenges in heterotic theory such as moduli stabilization and the determination of the full 4-dimensional, N=1 lagrangian (including the Kahler potential and normalized Yukawa couplings). Using the same mathematical toolkit outlined above, she will also study model building within global F-theory constructions. Despite being one of the most promising stringy approaches to particle phenomenology, F-theory is not fully understood. It is the goal to contribute to a rigorous framework for F-theory model building by systematically studying the geometry of Calabi-Yau 4-folds and the 2-dimensional cycles (or holes) within them that 7-branes wrap. In addition, the PI will explore new avenues of model building by introducing non-Abelian gauge field vacuum expectation values (vector bundles) over 7-brane stacks. Finally, the PI will study compact singular manifolds with G2 holonomy as backgrounds for M-theory and will also investigate the special (singular) points in 7-dimensional spaces of G2 holonomy (and their intersections), and derive the explicit 4-dimensional effective field theory of a compactification of M-theory in the neighborhood of these singularities. The PI hopes for the first time to produce globally defined G2 compactifications of M-theory. A combination of these three approaches should yield a new view of string phenomenology in string theory.
