The effective action of D6-branes in N=1 type IIA orientifolds

TL;DR

This work derives the four-dimensional effective action for a spacetime-filling D6-brane wrapped on a special Lagrangian cycle in a Type IIA Calabi–Yau orientifold. By performing a KK reduction within the democratic formulation and dualizing redundant RR degrees of freedom, the authors obtain explicit expressions for the Kähler potential, gauge kinetic functions, and a no-scale-compatible scalar potential, including a D-term that enforces the SLag calibration. They show that open-string moduli pair with brane fluctuations to form chiral coordinates, while brane moduli correct the complex-structure sector but not the Kähler sector at small fluctuations, in line with mirror symmetry expectations. A formal superpotential emerges from dualization, resembling flux-induced superpotentials, and the results are organized into an N=1 supergravity framework, highlighting the interplay between bulk and brane moduli and the calibration conditions. The analysis sets the stage for incorporating fluxes and using relative cohomology to treat the full open-closed moduli space, with potential phenomenological implications for gauge couplings and moduli stabilization.

Abstract

We use a Kaluza-Klein reduction to compute the low-energy effective action for the massless modes of a spacetime-filling D6-brane wrapped on a special Lagrangian 3-cycle of a type IIA Calabi-Yau orientifold. The modifications to the characteristic data of the N=1 bulk orientifold theory in the presence of a D6-brane are analysed by studying the underlying Type IIA supergravity coupled to the brane worldvolume in the democratic formulation and performing a detailed dualisation procedure. The N=1 chiral coordinates are found to be in agreement with expectations from mirror symmetry. We work out the Kahler potential for the chiral superfields as well as the gauge kinetic functions for the bulk and the brane gauge multiplets including the kinetic mixing between the two. The scalar potential resulting from the dualisation procedure can be formally interpreted in terms of a superpotential. Finally, the gauging of the Peccei-Quinn shift symmetries of the complex structure multiplets reproduces the D-term potential enforcing the calibration condition for special Lagrangian 3-cycles.