The N=1 effective actions of D-branes in Type IIA and IIB orientifolds

TL;DR

This paper derives the four-dimensional N=1 effective actions for D-branes in Type IIA and IIB Calabi-Yau orientifold compactifications, expressing key functions as chain integrals and relating moduli spaces via mirror symmetry.

Contribution

It provides explicit formulas for the Kähler potential, superpotential, and gauge couplings of D-branes, linking geometric deformations to effective field theory in a unified framework.

Findings

Effective actions depend on infinite deformations reduced to finite moduli spaces

Chain integral expressions for Kähler potentials are proposed

Mirror symmetry relates Type IIA and IIB D-brane moduli spaces

Abstract

We discuss the four-dimensional N=1 effective actions of single space-time filling Dp-branes in general Type IIA and Type IIB Calabi-Yau orientifold compactifications. The effective actions depend on an infinite number of normal deformations and gauge connection modes. For D6-branes the N=1 Kaehler potential, the gauge-coupling function, the superpotential and the D-terms are determined as functions of these fields. They can be expressed as integrals over chains which end on the D-brane cycle and a reference cycle. The infinite deformation space will reduce to a finite-dimensional moduli space of special Lagrangian submanifolds upon imposing F- and D-term supersymmetry conditions. We show that the Type IIA moduli space geometry is captured by three real functionals encoding the deformations of special Lagrangian submanifolds, holomorphic three-forms and Kaehler two-forms of Calabi-Yau manifolds. These elegantly combine in the N=1 Kaehler potential, which reduces after applying mirror symmetry to the results previously determined for space-time filling D3-, D5- and D7-branes. We also propose general chain integral expressions for the Kaehler potentials of Type IIB D-branes.