Abstract
The role of the \( \overline{\mathrm{D}3} \) brane in providing de Sitter vacua with spontaneously broken supersymmetry in the KKLT construction is clarified. The first step in this direction was explained in [1, 2]: it was shown there that in the GKP background the bosonic contributions to the vacuum energy from the DBI and WZ term cancel for a D3 brane, but double for a \( \overline{\mathrm{D}3} \) brane, leading to de Sitter vacua. The next step was taken in [3] where the analogous mechanism of the doubling (cancelation) of the \( \overline{\mathrm{D}3} \) (D3) DBI and WZ terms was discovered in the presence of Volkov-Akulov fermions living on the brane, in a flat supergravity background. Here we confirm this mechanism of doubling/cancelation for the \( \overline{\mathrm{D}3} \)/D3 brane in the GKP supergravity background preserving \( \mathcal{N} \) = 1, d = 4 supersymmetry. We find that imaginary self-dual G (3) flux of type (2, 1) nicely removes the SU(3) fermion triplet by giving it a large mass, while leaving the Volkov-Akulov goldstino, which is the SU(3) singlet, massless. This makes the de Sitter landscape in D-brane physics clearly related to de Sitter vacua in effective d = 4 supergravity with a nilpotent multiplet and spontaneously broken supersymmetry.
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Bergshoeff, E.A., Dasgupta, K., Kallosh, R. et al. \( \overline{\mathrm{D}3} \) and dS. J. High Energ. Phys. 2015, 58 (2015). https://doi.org/10.1007/JHEP05(2015)058
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DOI: https://doi.org/10.1007/JHEP05(2015)058