D terms from D-branes, gauge invariance and moduli stabilization in flux compactifications

TL;DR

This work analyzes how D-terms arise in ${\cal N}=1$ flux compactifications from D-branes and how they interplay with F-term moduli stabilization. Focusing on a concrete Type IIA setup with D6-branes at angles on $T^6/(Z_2\times Z_2)$ and O6-planes, NSNS/RR and geometric fluxes, it derives a D-term $D = N \mu_6 (\frac{n_1 n_2 n_3}{s} - \sum_{A} \frac{n_A m_B m_C}{u_A})$ and shows how axionic shift gauging from the D6-branes feeds into the four-dimensional potential. In a controlled two-derivative limit and under $|\mathrm{Im}\widetilde{\Omega}_\pi / \mathrm{Re}\widetilde{\Omega}_\pi| \ll 1$, the D-term part matches the standard ${\cal N}=1$ D-term with gauge kinetic function $f = N T_6 (p_0 S - \sum_A p_A U_A)$, linking brane-induced gaugings to the bulk theory. The analysis is extended to other ${\cal N}=1$ compactifications and non-geometric fluxes, clarifying consistency with localized Bianchi identities and Freed-Witten anomalies, and the work discusses the potential role of U(1) D-terms in bulk moduli stabilization and vacuum structure (AdS$_4$ and Minkowski) in flux vacua.

Abstract

We elucidate the structure of D terms in N=1 orientifold compactifications with fluxes. As a case study, we consider a simple orbifold of the type-IIA theory with D6-branes at angles, O6-planes and general NSNS, RR and Scherk-Schwarz geometrical fluxes. We examine in detail the emergence of D terms, in their standard supergravity form, from an appropriate limit of the D-brane action. We derive the consistency conditions on gauged symmetries and general fluxes coming from brane-localized Bianchi identities, and their relation with the Freed-Witten anomaly. We extend our results to other N=1 compactifications and to non-geometrical fluxes. Finally, we discuss the possible role of U(1) D terms in the stabilization of the untwisted moduli from the closed string sector.