Abstract
Gaugino condensation plays a crucial role in the formation of de Sitter vacua. However, the theory of this effect is still incomplete. In four dimensions, the perfect square nature of gaugino couplings follows from the square of auxiliaries in the supergravity action. We explain here why the supersymmetric non-Abelian Dp-brane action, which is the basis for the theory of ten-dimensional gaugino condensation, must have a four-gaugino coupling. This term in the Einstein-Yang-Mills ten-dimensional supergravity is a part of the perfect square, mixing a 3-form with a gaugino bilinear. The perfect square term follows from the superspace geometry, being a square of the superspace torsion. The supercovariant equation of motion for a gaugino on the non-Abelian Dp-brane also involves a supertorsion in agreement with the perfect square term in the action.
Highlights
The issue of supersymmetry in Dp-brane actions is well understood for a single Dp-brane
When this local κ symmetry is gauge fixed as in Refs. [4,5], one recovers the Abelian supersymmetric Dpbrane action, which breaks the maximal supersymmetry of type-II supergravity, half of it being realized linearly
In general 4D supergravity, the role of gaugino condensates with regard to spontaneous breaking of local supersymmetry was explained in Ref. [24] based on the properties of the auxiliary fields Fα of the chiral multiplets discovered in Ref. [25]
Summary
The issue of supersymmetry in Dp-brane actions is well understood for a single Dp-brane. [6,7,8,9,10] in this context This issue attracted some attention after the recent ten-dimensional (10D) investigation of the Kachru, Kallosh, Linde, Trivedi (KKLT) mechanism [34] in Ref. [11,12] was the absence of the four-fermion nonderivative coupling on D7-branes This assumption was recently challenged in Ref. We will explain why the non-Abelian generalization of Dp-brane action must have a four-fermion nonderivative coupling. The perfect square structure underlying these features of the Dp-branes is a consequence of the superspace geometry These results are quite general; they apply to type-IIB theory and to the KKLT scenario. They support and further develop the proposal made in Ref. [18]
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