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

TL;DR

This work derives the four-dimensional $\mathcal{N}=1$ effective action for a single spacetime-filling D6-brane in Type IIA Calabi–Yau orientifolds, including the infinite open-string deformation spectrum and Wilson-line modes. The authors show the open–closed moduli space is elegantly encoded by Hitchin functionals and chain-integral constructions, yielding a unified $\mathcal{N}=1$ Kahler potential $K=K^{\rm ks}+K^{\rm Q}$ and a holomorphic brane gauge coupling, with D- and F-term potentials arising from general deformations via a D-term gauging and a superpotential $W=\int_{\mathcal{C}_4}(J_c-\mathcal{F}_{D6})\wedge(J_c-\mathcal{F}_{D6})$. They extend the analysis to finite deformations, discuss the mixing between brane and bulk vectors, and establish mirror-symmetric expressions for Type IIB D3/D5/D7-branes using the SYZ framework. The results bridge open- and closed-string dynamics and provide chain-integral tools potentially useful for computing quantum corrections and for connecting to M-theory on $G_2$ manifolds.

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.