Abstract
We study the supersymmetry breaking induced by probe anti-D3-branes at the tip of the Klebanov-Strassler throat geometry. Antibranes inside this geometry polarize and can be described by an NS5-brane wrapping an $S^2$. When the number of antibranes is small compared to the background flux a metastable state exists that breaks supersymmetry. We present a manifestly supersymmetric effective model that realizes the polarized metastable state as a solution, spontaneously breaking the supersymmetry. The supersymmetric model relies crucially on the inclusion of Kaluza-Klein (matrix) degrees of freedom on the $S^2$ and two supersymmetric irrelevant deformations of ${\cal N}=4$ super-Yang-Mills (SYM), describing a large number of supersymmetric D3-branes in the IR. We explicitly identify the massless Goldstino and compute the spectrum of massive fluctuations around the metastable supersymmetry-breaking minimum, finding a Kaluza-Klein tower with masses warped down from the string scale. Below the Kaluza-Klein scale the massive tower can be integrated out and supersymmetry is realized nonlinearly. We comment on the effect of the Kaluza-Klein modes on the effective description of de Sitter vacua in string theory and inflationary model building.
Highlights
Antibranes in a flux background are a key ingredient in many of the constructions of de Sitter vacua in string theory
When the number of antibranes is small compared to the background flux a metastable state exists that breaks supersymmetry
In the previous section we argued that neither of the probe actions used by KPV preserve linear supersymmetry when placed inside the KS background
Summary
Antibranes in a flux background are a key ingredient in many of the constructions of de Sitter vacua in string theory. Energies the massive fields can be integrated out and a single Goldstino remains that can be described by a nilpotent chiral superfield This yields a low-energy effective action that enjoys nonlinear supersymmetry, valid below the cutoff scale set by the masses of the superpartners that are projected out by the constraint [43]. We will address this question and present an effective supersymmetric model obtained by deforming N 1⁄4 4 SYM by irrelevant deformations that preserve N 1⁄4 1 supersymmetry This model contains a metastable vacuum state very similar to the metastable state of [49] and breaks supersymmetry spontaneously by a nonzero F-term. IV and discuss the implications of our results for metastable de Sitter vacua in string theory and inflationary model building
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