Understanding KKLT from a 10d perspective
  Some of the most well-celebrated constructions of metastable de Sitter vacua
from string theory, such as the KKLT proposal, involve the interplay of gaugino
condensation on a D7-brane stack and an uplift by a positive tension object.
These constructions have recently been challenged using arguments that rely on
the trace-reversed and integrated 10d Einstein equation. We give a critical
assessment of such concerns. We first relate an integrated 10d Einstein
equation to the extremization condition for a 10d-derived 4d effective
potential. Then we argue how to obtain the latter from a 10d action which
incorporates gaugino condensation in a (recently proposed) manifestly finite,
perfect-square form. This effective potential is consistent with 4d
supergravity and does not present obstacles for an uplifted minimum. Moreover,
within standard approximations, we understand the uplift explicitly in one of
the popular versions of the integrated 10d equation. Our conclusion is that de
Sitter constructions of the KKLT type cannot be dismissed simply based on the
integrated 10d equations considered so far.
