  Anti-D3 branes and non-perturbative effects in flux compactifications
spontaneously break supersymmetry and stabilise moduli in a metastable de
Sitter vacua. The low energy 4D effective field theory description for such
models would be a supergravity theory with non-linearly realised supersymmetry.
Guided by string theory modular symmetry, we compute this non-linear
supergravity theory, including dependence on all bulk moduli. Using either a
constrained chiral superfield or a constrained vector field, the uplifting
contribution to the scalar potential from the anti-D3 brane can be
parameterised either as an F-term or Fayet-Iliopoulos D-term. Using again the
modular symmetry, we show that 4D non-linear supergravities that descend from
string theory have an enhanced protection from quantum corrections by
non-renormalisation theorems. The superpotential giving rise to metastable de
Sitter vacua is robust against perturbative string-loop and $\alpha'$
corrections.
