Gaugino Condensates and D-terms from D7-branes
Michael Haack, Daniel Krefl, Dieter Lust, Antoine Van Proeyen, Marco Zagermann
TL;DR
The paper constructs a microscopic type IIB D-brane framework in which a D7-brane with world-volume flux generates a D-term that can uplift an AdS vacuum, while a separate D7 stack undergoes gaugino condensation. It shows that if the Kähler modulus of the gaugino-condensing cycle is charged under the anomalous U(1)_F, the non-perturbative ADS-like superpotential can remain gauge invariant thanks to an index-counted set of bifundamental matter and Green-Schwarz anomaly cancellation. The authors derive the D-term from the D7 DBI action, identify how axion shifts are gauged, and demonstrate that higher curvature corrections do not spoil the charge structure essential for invariance. Together, these results provide a concrete microscopic mechanism to realize D-term uplifts in KKLT-type scenarios, albeit with caveats about global model-building and open-string sector details.
Abstract
We investigate, at the microscopic level, the compatibility between D-term potentials from world-volume fluxes on D7-branes and non-perturbative superpotentials arising from gaugino condensation on a different stack of D7-branes. This is motivated by attempts to construct metastable de Sitter vacua in type IIB string theory via D-term uplifts. We find a condition under which the Kaehler modulus, T, of a Calabi-Yau 4-cycle gets charged under the anomalous U(1) on the branes with flux. If in addition this 4-cycle is wrapped by a stack of D7-branes on which gaugino condensation takes place, the question of U(1)-gauge invariance of the (T-dependent) non-perturbative superpotential arises. In this case an index theorem guarantees that strings, stretching between the two stacks, yield additional charged chiral fields which also appear in the superpotential from gaugino condensation. We check that the charges work out to make this superpotential gauge invariant, and we argue that the mechanism survives the inclusion of higher curvature corrections to the D7-brane action.