Anti-D3 branes and moduli in non-linear supergravity

TL;DR

This paper derives a non-linear supergravity framework for anti-D3 branes in flux compactifications, showing it is robust against quantum corrections and consistent with string theory symmetries.

Contribution

It provides a detailed computation of the non-linear supergravity theory including all moduli dependence, connecting string theory constructions with effective field theory descriptions.

Findings

The uplifting contribution can be modeled as an F-term or D-term.

The supergravity theory is protected from quantum corrections by non-renormalisation theorems.

The superpotential remains stable against string-loop and $ ext{α'}$ corrections.

Abstract

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.