Warping and F-term uplifting

TL;DR

This work analyzes warped IIB compactifications with D3- and D7-branes to understand how warping affects moduli stabilization and SUSY breaking. The authors show that warping suppresses $F$-terms but leaves $D$-terms largely unchanged, implying that small positive cosmological constants from strong warping require nearly vanishing $D$-terms and rely on $F$-term uplifting. They study magnetised D7-brane setups producing gaugino condensation and find Minkowski vacua with $D \approx 0$ are hard to realize for credible parameter ranges, motivating the inclusion of an ISS sector to uplift AdS minima. When an ISS sector is coupled, the uplift can yield a small gravitino mass for moderate warping, with $e^{-A_0} \sim 10^{-5}$, offering a concrete route toward low-scale SUSY in string-inspired models. Overall, the paper provides a detailed mapping of warping’s impact on the Kähler potential, superpotential, and $D$-terms, establishing practical criteria for achieving controlled uplift in warped flux compactifications.

Abstract

We analyse the effective supergravity model of a warped compactification with matter on D3 and D7-branes. We find that the main effect of the warp factor is to modify the F-terms while leaving the D-terms invariant. Hence warped models with moduli stabilisation and a small positive cosmological constant resulting from a large warping can only be achieved with an almost vanishing D-term and a F-term uplifting. By studying string-motivated examples with gaugino condensation on magnetised D7-branes, we find that even with a vanishing D-term, it is difficult to achieve a Minkowski minimum for reasonable parameter choices. When coupled to an ISS sector the AdS vacua is uplifted, resulting in a small gravitino mass for a warp factor of order 10^-5.