The effective action of D7-branes in N=1 Calabi-Yau orientifolds

TL;DR

This paper derives the four-dimensional N=1 effective action for D7-branes on generic Calabi-Yau orientifolds, detailing the Kähler potential, gauge kinetic functions, and scalar potential based on geometrical data.

Contribution

It provides a general computation of the D7-brane effective action without relying on a specific orientifold, linking it to N=1 special geometry and analyzing D-term structures.

Findings

Derived the Kähler potential, gauge kinetic functions, and scalar potential for D7-branes.

Connected the D-brane couplings to bulk moduli and N=1 special geometry.

Commented on the D-term structure induced by Green-Schwarz mechanism.

Abstract

Using a Kaluza-Klein reduction of the Dirac-Born-Infeld and Chern-Simons action we compute the four dimensional N=1 effective action for the massless modes of a D7-brane which is wrapped on a four-cycle of a compact Calabi-Yau orientifold. We do not consider a specific orientifold but instead determine the Kahler potential, the gauge kinetic functions and the scalar potential in terms of geometrical data of a generic orientifold and its wrapped four-cycle. In particular we derive the couplings of the D-brane excitations to the bulk moduli of the orientifold as they are important for the study of soft supersymmetry breaking terms. We relate the resulting Kahler geometry to the N=1 special geometry of Lerche, Mayr and Warner. Finally we comment on the structure of the D-term which is induced by a Green-Schwarz term in the Chern-Simons action.