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

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 Kahler 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 suhmanifolds upon imposing F- and D-term supersymmetry conditions. We show that the Type HA moduli space geometry is captured by three real functionals encoding the deformations of special Lagrangian submanifolds, holomorphic three-forms and Kahler two-forms of Calabi-Yau manifolds. These elegantly combine in the N = 1 Kahler potential, which reduces after applying mirror symmetry to the results previously determined for space-time filling D3-. D5- and D7-hranes. We also propose general chain integral expressions for the Kahler potentials of Type IIB D-branes. (C) 2011 Elsevier B.V. All rights reserved.