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.
Highlights
One may view this observation as a first indication that the complete brane action with account of fermions which live on the brane, might exhibit an analogous phenomenon: cancelation of the DBI and WZ terms for the D3 brane and doubling for the D3 brane in the GKP background [4] preserving N = 1 supersymmetry
In this paper we studied the action of a single D3 brane in a GKP background [4], preserving N = 1 supersymmetry
We are using the orientifolding condition imposed on fermions, θ2 = Γ0123θ1, with and without truncation from the spectrum the worldvolume scalar fields and the vector. Such a truncation of the bosonic degrees of freedom was suggested by the fact that the D3 brane under the same orientifold condition on the fermions does not have a kinetic term for the fermions, all bosons have to be cut off, both on the D3 brane as well as on the D3 brane
Summary
The interest in the Volkov-Akulov supersymmetry [16, 17] was renewed recently because of its application to cosmology which started in [27]. We would like to keep the following issue in mind: in the flat background we have found it useful in [3] to impose the orientifold condition on spinors (2.14) and bosons (2.15), to obtain a consistent supersymmetric truncation of the D3 and D3 brane actions. Such a truncation corresponds to a D3 or D3 brane on top of an O3 plane. We will study the corresponding fermionic action in the two subsections
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