KKLTtype

KKLT-type constructions are a class of proposals in type IIB string theory for stabilizing all moduli and obtaining metastable de Sitter vacua in four dimensions. They rely on compactifications of orientifolded Calabi-Yau manifolds with background fluxes that generate a superpotential stabilizing the complex structure moduli and the dilaton. In these scenarios the flux superpotential W0 fixes the shape and coupling constants at a supersymmetric minimum, while the Kähler moduli remain unfixed at this stage. Non-perturbative effects, such as gaugino condensation on stacks of D7-branes or Euclidean D3-brane instantons, generate a non-perturbative contribution to the superpotential that stabilizes the overall volume modulus in an anti-de Sitter vacuum with N=1 supersymmetry.

To obtain a universe with a small positive cosmological constant, an anti-D3-brane is placed in a strongly warped region of the compactification, providing a small positive energy that lifts the AdS minimum to a metastable de Sitter minimum. The resulting vacuum has broken supersymmetry, with the gravitino mass and SUSY-breaking scale determined by the stabilization data and warping. A common simplified parametrization uses W = W0 + A e^{-aT}, where T is the Kähler modulus and W0 is tuned to achieve the desired uplift.

KKLT-type constructions have been influential in string phenomenology and cosmology as concrete mechanisms for moduli stabilization and SUSY breaking. They face criticisms related to the required fine-tuning, potential backreaction of the uplift, and questions about the global consistency and stability of de Sitter vacua. Related approaches include the Large Volume Scenario and racetrack models, which realize stabilization and uplifting through different dynamics and energy scales.