### abstract

- This award funds the research activities of Professors Katrin Becker, Melanie Becker, and Ergin Sezgin at Texas A&M University.String theory provides a framework for describing gravity in a way which is consistent with the laws of quantum mechanics. However, string theories generally require that there exist extra dimensions beyond those of width, length, and height. Such extra dimensions must be rolled into very small spaces, and the shapes of these spaces determine which elementary particles are predicted by string theory. For these reasons, it is important to understand the detailed shapes of these extra dimensions. Likewise, combining Einstein''s theory of gravity with quantum mechanics involves a hypothetical particle --- the so-called "graviton" --- which transmits gravitational interactions and carries two units of spin. However, string theory can also give rise to remarkable extensions of Einstein''s theory which involve higher-spin analogues of the graviton. For these reasons, string theory can have profound consequences for early-universe physics. In their research, Professors Becker, Becker, and Sezgin aim to investigate these and other fundamental questions involving the connections between string theory, gravity, and higher-spin theories. As such, this project advances the national interest by promoting progress in fundamental science within the United States. This project is also envisioned to have significant broader impacts. Not only will this research further develop the interface between string theory and mathematics, but it will also provide an arena for the critical training for postdocs and students. Professors Becker, Becker, and Sezgin will also give public lectures on their research results and organize scientific workshops to help advance the field.More technically, Professors Becker, Becker, and Sezgin aim to construct the full spacetime effective action of different string theory and M-theory compactifications to all orders in the slope parameter and its formulation in superspace. Their goal is to use physical ideas and methods to solve long-standing problems in mathematics. Further, Professors Becker, Becker, and Sezgin will study the holographic description of higher-spin theory, its coupling to matter, spontaneous symmetry breaking, cosmological solutions and their consequences for early-universe physics. They will also study specific aspects of a geometrical description of duality symmetries of strings and branes within a framework known as exceptional field theory.This award reflects NSF''s statutory mission and has been deemed worthy of support through evaluation using the Foundation''s intellectual merit and broader impacts review criteria.