D-Terms from Generalized NS-NS Fluxes in Type II

TL;DR

This work develops a unified four-dimensional N=1 supergravity framework incorporating generalized NS-NS fluxes (H, metric, and non-geometric Q/R fluxes) in Type II orientifolds. It demonstrates how these fluxes can act as electric and magnetic charges for R-R axions, generating D-term contributions to the scalar potential in both IIA and IIB setups, and provides explicit formulae for the superpotential and D-terms. The authors derive Bianchi identities, tadpole constraints, and mutual locality conditions, and illustrate the construction with concrete IIB examples, including an O3/O7 model on T^6/Z4 and its O5/O9 dual. The results suggest that D-terms from generalized NS-NS fluxes can enrich moduli stabilization and possibly inform slow-roll inflation or de Sitter vacua, while highlighting challenges related to flux quantization and higher-dimensional consistency. Overall, the paper offers a detailed toolkit for embedding D-terms into flux compactifications and demonstrates the practical viability of including generalized NS-NS fluxes in the 4D effective theory.

Abstract

Orientifolds of type II string theory admit a certain set of generalized NS-NS fluxes, including not only the three-form field strength H, but also metric and non-geometric fluxes, which are related to H by T-duality. We describe in general how these fluxes appear as parameters of an effective N=1 supergravity theory in four dimensions, and in particular how certain generalized NS-NS fluxes can act as charges for R-R axions, leading to D-term contributions to the effective scalar potential. We illustrate these phenomena in type IIB with the example of a certain orientifold of T^6/Z_4.