F Theory Compactifications and Central Charges of BPS States

F-theory, as Theory of everything is compactified on Calabi-Yau threefolds or fourfolds. Using Batyrev’s toric approximation and mirror symmetry of Calabi-Yau manifolds it is possible to present Calabi-Yau in the form of dual integer polyhedra. With the help of Gelfand, Zelevinsky, Kapranov algorithm are calculated the numbers of BPS-states in F-theory, and by application of Tate’s algorithm are determined the enhanced symmetries. As the result, any integral dual polyhedron representing a Calabi-Yau manifold, is characterized by its own set of topological invariants - the numbers of BPS-states, whose central charges are classified by enhanced symmetries.