D 3 ¯ $$ \overline{\mathrm{D}3} $$ and dS

Abstract

The role of the 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 [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 D3 brane, leading to de Sitter vacua. The next step was taken in [3] where the analogous mechanism of the doubling (cancelation) of the 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 D3/D3 brane in the GKP supergravity background preserving 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.

Pure de Sitter supergravity

“…The elegant geometric Lagrangian of the original form of the VA theory involves the determinant of a quadratic form in the Goldstino, L ¼ Detðδ μ ν þχγ μ ∂ ν χÞ. It is known how to couple it to a supergravity background in the D-brane actions; however, the corresponding supersymmetry upon gauge-fixing local κ-symmetry is still a rigid supersymmetry [4,5]. It would be useful to know whether de Sitter supergravity with local supersymmetry presented in this paper may be brought to the geometric form of the global VA theory: this could generate further insights into the nature of fundamental symmetries and the origin of the positive cosmological constant.…”

“…Towards this end we consider the wave equation on S 4 which is the Wick rotation of dS 4 . The radius of the sphere is given by H 2 ¼ κ 2 Λ=3.…”

“…It was recently updated to the status of a manifestly supersymmetric uplifting using the D3-brane on top of an O3-plane at the bottom of a warped throat [4,5]. It corresponds to a globally supersymmetric Volkov-Akulov (VA) Goldstino theory [6] coupled to a supergravity background.…”

“…It is then convenient 4 to redefine our parameters as follows: a ¼ κm and b ¼ κ 2 f. The new parameters m and f have mass dimension 1 and 2, respectively, and we take them to be real. 5 The cosmological constant Λ and the Lagrangian mass term of the gravitino are…”

Interactions ofNGoldstini in Superspace

“…This might also help finding new interesting scenarios for inflationary cosmology, providing new models with non-linear realizations of supersymmetry along the lines of [39]- [44]. Finally, while one might suspect that ultraviolet completions within string theory may exist only for special values of N , it would be interesting to understand which string compactifications may give rise to such non-linear realizations [45]- [49].…”