Moduli stabilization with positive vacuum energy

Abstract

We study the effect of anomalous U (1) gauge groups in string theory compactification with fluxes. We find that, in a gauge invariant formulation, consistent AdS vacua appear breaking spontaneously supergravity. Non vanishing D-terms from the anomalous symmetry act as an uplifting potential and could allow for de Sitter vacua. However, we show that in this case the gravitino is generically (but not always) much heavier than the electroweak scale. We show that alternative uplifting scheme based on corrections to the Kahler potential can be compatible with a gravitino mass in the TeV range.

Warping and F-term uplifting

“…We study the string inspired examples where the moduli stabilisation superpotential results from the presence of magnetised D7-branes with a chiral spectrum and gaugino condensation [8]. We find no consistent Minkowski solutions with vanishingly small Dterms, as needed for low scale SUSY breaking.…”

“…Together with W 0 , this provides a stabilising potential for the volume modulus T . In addition we introduce a direct coupling between the chiral matter fields [8]W…”

“…The corresponding transformations for the quarks and antiquarks living on the magnetised brane, and the SU(N ) singlet, are respectively δΦ i = iq 1 ǫΦ i , δΦ i = iq 1 ǫΦ i , and δΞ = −iǫΞ. The required cancellation condition for the SU(N ) 2 × U(1) X anomaly is 8) and the one for the U(1) 3 X anomaly is…”

“…Furthermore, we assume that the quarks are light and cannot be integrated out. Taking inspiration from [8], we will consider the limit χ 2 ≪ m 2 Pl and T ≫ 1. Then the dominant contributions to the potential are V D and…”

“…But the price to pay is that the uplifting term is naturally of order one in Planck units, giving rise to a large gravitino mass m 3/2 ∼ m Pl /(8π) and thus to high scale SUSY breaking. Uplifting mechanisms using F -terms have also been analysed [7,8,9], and models exist that are supersymmetric and have a small gravitino mass [10,11].…”