D7-Brane Moduli vs. F-Theory Cycles in Elliptically Fibred Threefolds

TL;DR

This paper explores the relationship between D7-brane moduli and F-theory cycles in elliptically fibred threefolds, establishing a topological correspondence in the context of type IIB compactifications.

Contribution

It provides a topological construction linking D7-brane moduli to F-theory threefold cycles, demonstrating a complete match in degrees of freedom in a general setting.

Findings

Complete agreement between D7-brane moduli and F-theory complex structure deformations.

Construction of 3-cycles in F-theory from D7-brane topology.

Results applicable to general base spaces in elliptic Calabi-Yau threefolds.

Abstract

We study the space of geometric and open string moduli of type IIB compactifications from the perspective of complex structure deformations of F-theory. In order to find a correspondence, we work in the weak coupling limit and for simplicity focus on compactifications to 6 dimensions. Starting from the topology of D7-branes and O7-planes, we construct the 3-cycles of the F-theory threefold. We achieve complete agreement between the degrees of freedom of the Weierstrass model and the complex structure deformations of the elliptic Calabi-Yau. All relevant quantities are expressed in terms of the topology of the base space, allowing us to formulate our results for general base spaces.