String theory provides consistent high-energy extrapolations of theoretical models of particle physics, as well as naturally unifying those models with gravity, and provides tools of mathematical physics with a number of applications in theoretical physics. One promising type of string theory model known as F-theory has seen a resurgence of interest in recent years which points out the need for some basic foundational studies. These studies involve a sophisticated branch of mathematics, algebraic geometry, which provides the background for constructing the physical models. The PI will determine what are the restrictions for gauge groups and matter content for F-theory models, both on Calabi-Yau threefolds and Calabi-Yau fourfolds; whether every elliptically-fibered Calabi-Yau fourfold is birational to an equidimensional family, and if not, what is the physical interpretation of the fibers of large dimension; the structure of the base of an elliptically fibered Calabi-Yau manifold; the F-theory interpretation of Calabi-Yau manifolds which have a genus one fibration that is not elliptic (i.e., there is no section); how the birational geometry of the total space of an elliptically fibered Calabi-Yau fourfold interacts with the choices of flux on that fourfold, and in particular, to what extent F-theory vacua are necessarily lifted by fluxes; the M-theory dual interpretation of the theory of T-branes; can the duality between F-theory and nongeometric heterotic strings be extended; and other topics in Calabi-Yau geometry which may be relevant to F-theory, including further exploration of the recent discovery that the gauged linear sigma models which describe Calabi-Yau manifolds contain via a partition function on S2 a wealth of information about the Calabi-Yau manifold. Broader Impact The project will also have a broader impact through educational activities of the PI, at the undergraduate, graduate and postdoctoral levels, as well as through the PI's ongoing efforts to streamline scientific communication by making as much of it available electronically as possible.
