$\overline{\rm D3}$ and dS

TL;DR

This paper clarifies how anti-D3 branes contribute to de Sitter vacua in string theory by analyzing their interactions in a supergravity background, confirming a mechanism that relates string theory constructions to effective supergravity models with broken supersymmetry.

Contribution

It confirms the doubling/cancellation mechanism of brane contributions in GKP backgrounds with supersymmetry, connecting string theory de Sitter vacua to supergravity with a nilpotent multiplet.

Findings

Imaginary self-dual flux removes the SU(3) fermion triplet massively.

The Volkov-Akulov goldstino remains massless.

The mechanism links string theory de Sitter vacua to supergravity models with broken supersymmetry.

Abstract

The role of the $\overline{\rm D3}$ 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 arXiv:hep-th/0301240, arXiv:hep-th/0308055: 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 $\overline{\rm D3}$ brane, leading to de Sitter vacua. The next step was taken in arXiv:1411.1121 where the analogous mechanism of the doubling (cancelation) of the $\overline{\rm D3}$ (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 $\overline{\rm D3}$/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.