Moduli stabilisation and de Sitter string vacua from magnetised D7 branes

Anomalous U(1)'s are ubiquitous in 4D chiral string models. Their presence crucially affects the process of moduli stabilisation and cannot be neglected in realistic set-ups. Their net effect in the 4D effective action is to induce a matter field dependence in the non-perturbative superpotential and a Fayet-Iliopoulos D-term. We study flux compactifications of IIB string theory in the presence of magnetised D7 branes. These give rise to anomalous U(1)'s that modify the standard moduli stabilisation procedure. We consider simple orientfold models to determine the matter field spectrum and the form of the effective field theory. We apply our results to one-modulus KKLT and multi-moduli large volume scenarios, in particular to the Calabi-Yau IP[1,1,1,6,9]4. After stabilising the matter fields, the effective action for the Kahler moduli can acquire an extra positive term that can be used for de Sitter lifitng with non-vanishing F- and D-terms. This provides an explicit realization of the D-term lifting proposal of [1].