Gaugino Condensates and D-terms from D7-branes

TL;DR

This paper examines the compatibility of D-term potentials from D7-branes with non-perturbative superpotentials from gaugino condensation in type IIB string theory, ensuring gauge invariance and stability for de Sitter vacua.

Contribution

It provides a detailed analysis of the conditions under which D-term potentials and gaugino condensation can coexist consistently in string compactifications.

Findings

Charged Kaehler moduli under anomalous U(1) are identified.

Charged chiral fields from strings ensure superpotential gauge invariance.

The mechanism remains valid with higher curvature corrections.

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.