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Résumé |
With a view towards string cosmology and de Sitter vacua, I will consider a probe anti-D3 brane in a supersymmetric flux compactification with non-perturbative effects. Postponing questions of backreaction, singularities and tachyons, the anti-D3 brane spontaneously breaks supersymmetry and the effective field theory describing the system at low energies is a supergravity theory with non-linearly realised supersymmetry. \par Guided by string theory modular symmetry, I will show how to 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 $\alpha ^\prime$ corrections. |
