F-theory compactifications and central charges of BPS-states

TL;DR

This paper explores F-theory compactifications on Calabi-Yau manifolds, using toric geometry and mirror symmetry to compute BPS-state counts and classify their central charges via enhanced symmetries.

Contribution

It introduces a method to determine BPS-state numbers and symmetries of Calabi-Yau compactifications using toric approximation and mirror symmetry techniques.

Findings

Calculated BPS-state numbers for Calabi-Yau manifolds.

Identified enhanced symmetries via Tate algorithm.

Characterized topological invariants of dual polyhedra.

Abstract

F-theory, as Theory of Everything is compactified on Calabi-Yau threefolds or fourfolds. Using toric approximation of Batyrev 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 were calculated the numbers of BPS-states in F-theory, and by application of Tate algorithm were 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.