Anti-D3 branes and moduli in non-linear supergravity
Maria Garcia del Moral (Departamento de Fisica, Universidad de Antofagasta, Antonio Toro 851, Casilla 170, Antofagasta, Chile); Susha Parameswaran (Department of Mathematical Sciences, University of Liverpool, Peach Street, Liverpool, L69 7ZL, U.K.); Norma Quiroz (Departamento de Ciencias de la Naturaleza, CUSUR, Universidad de Guadalajara, Enrique Arreola Silva 883, C.P. 49000, Cd. Guzmán, Jalisco, México); Ivonne Zavala (Department of Physics, Swansea University, Swansea, Singleton Park, SA2 8PP, U.K.)
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 α ′ corrections.
