Gaugino condensates andD-terms from D7-branes

We investigate, at the microscopic level, the compatibility between D-termpotentials from world-volume fluxes on D7-branes and non-perturbativesuperpotentials arising from gaugino condensation on a different stack ofD7-branes. This is motivated by attempts to construct metastable de Sittervacua in type IIB string theory via D-term uplifts. We find a condition underwhich the Kaehler modulus, T, of a Calabi-Yau 4-cycle gets charged under theanomalous U(1) on the branes with flux. If in addition this 4-cycle is wrappedby a stack of D7-branes on which gaugino condensation takes place, the questionof U(1)-gauge invariance of the (T-dependent) non-perturbative superpotentialarises. In this case an index theorem guarantees that strings, stretchingbetween the two stacks, yield additional charged chiral fields which alsoappear in the superpotential from gaugino condensation. We check that thecharges work out to make this superpotential gauge invariant, and we argue thatthe mechanism survives the inclusion of higher curvature corrections to theD7-brane action.Comment: 34 pages, 1 figure, LaTeX2e; References added, open issue concerning higher derivative corrections clarified, other minor change