Emergence of spontaneously broken supersymmetry on an anti-D3-brane in KKLT dS vacua

Abstract

The KKLT construction of de Sitter vacua includes an uplifting term coming from an anti-D3-brane. Here we show how this term can arise via spontaneous breaking of supersymmetry, based on the emergence of a nilpotent chiral supermultiplet on the worldvolume of the anti-D3-brane. We establish and use the fact that both the DBI as well as the WZ term, with account of orientifolding, acquire a form of the Volkov-Akulov action. For an O3 orientifold involution of R 9,1 we demonstrate the cancellation between the fermionic parts of the DBI and WZ term for the D3-brane action. For the anti-D3-brane we show that the DBI action and the WZ action combine and lead to the emergence of the goldstino multiplet which is responsible for spontaneous breaking of supersymmetry. This provides a string theoretic explanation for the supersymmetric uplifting term in the KKLT effective supergravity model supplemented by a nilpotent chiral multiplet.

D 3 ¯ $$ \overline{D3} $$ induced geometric inflation

“…Note that at the minimum ϕ = 0, the axion mass squared becomes 4W 2 0 = 4m 2 3/2 . If we take a more general function 16) and the potential is…”

“…Its worldvolume theory includes a Volkov-Akulov fermion goldstino [3,4], which can be equivalently described in terms of a nilpotent scalar superfield S with S 2 (x, θ) = 0 [5][6][7][8][9][10][11][12][13][14][15]. This nilpotent superfield allows for a manifestly supersymmetric description of the uplift to a de Sitter minimum [16][17][18][19][20][21][22][23]. In a parallel development, it has been realized that nilpotent superfields have great potential as a model building tool in effective supergravity theories of inflation [24][25][26][27][28].…”

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

“…These actions after gauge-fixing of the local fermionic κ-symmetry have spontaneously broken supersymmetry in the presence of the fermions remaining on the brane after the gauge-fixing. The corresponding analysis of the actions was performed in [3] in a flat supergravity background. 1 It was shown that in the presence of fermions, under certain orientifolding conditions, the cancelation of the DBI and WZ terms on the D3 brane and doubling on the D3 take place in the exact nonlinear expression with fermions.…”

“…The fermion action is a Volkov-Akulov goldstino action [16,17], as expected according to [11], in a flat background. The result of [3] is…”

“…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.…”