KKLT

KKLT refers to a framework proposed in 2003 by Kachru, Kallosh, Linde, and Trivedi for stabilizing all moduli in flux compactifications of type IIB string theory and for obtaining metastable de Sitter vacua. The construction operates within four-dimensional N=1 supergravity derived from Calabi–Yau orientifolds with background fluxes.

First, background fluxes generate a Gukov-Vafa-Witten superpotential W0 that fixes the complex structure moduli and the dilaton, leaving the Kahler moduli unfixed. Non-perturbative effects, such as gaugino condensation on D7-branes or Euclidean D3-brane instantons, produce a non-perturbative superpotential W_np = A e^{-a T}, stabilizing the overall Kahler modulus T and yielding a supersymmetric anti-de Sitter (AdS) minimum.

To obtain a positive cosmological constant, the solution is uplifted by introducing a small number of anti-D3-branes in a highly warped region (throat). The SUSY-breaking effect of the anti-brane raises the AdS minimum to a metastable de Sitter minimum. In practice, achieving a tiny positive vacuum energy requires tuning of parameters, notably W0 and the coefficients in W_np, to control the height of the uplift.

KKLT has been highly influential, shaping discussions of the string landscape and the possible existence of de Sitter vacua in string theory. It has also faced debate, including concerns about the backreaction and consistency of anti-D3-brane uplifting, sensitivity to approximations, and challenges from swampland conjectures. Subsequent approaches to moduli stabilization, such as the Large Volume Scenario, offer alternative routes to de Sitter-like vacua within similar frameworks.