Moduli stabilisation and de Sitter string vacua from magnetised D7 branes

Anomalous U(1)'s are ubiquitous in 4D chiral string models. Their presencecrucially affects the process of moduli stabilisation and cannot be neglectedin realistic set-ups. Their net effect in the 4D effective action is to inducea matter field dependence in the non-perturbative superpotential and aFayet-Iliopoulos D-term. We study flux compactifications of IIB string theoryin the presence of magnetised D7 branes. These give rise to anomalous U(1)'sthat modify the standard moduli stabilisation procedure. We consider simpleorientifold models to determine the matter field spectrum and the form of theeffective field theory. We apply our results to one-modulus KKLT andmulti-moduli large volume scenarios, in particular to the Calabi-YauP^4_{[1,1,1,6,9]}. After stabilising the matter fields, the effective actionfor the Kahler moduli can acquire an extra positive term that can be used forde Sitter lifting with non-vanishing F- and D-terms. This provides an explicitrealization of the D-term lifting proposal of hep-th/0309187.Comment: 35 pages, 1 figure. v2: Minor changes, references adde