Abstract
In this work we study ten-dimensional solutions to type IIA string theory of the form AdS4 × X6 which contain orientifold planes and preserve mathcal{N} = 1 supersymmetry. In particular, we consider solutions which exhibit some key features of the four-dimensional DGKT proposal for compactifications on Calabi-Yau manifolds with fluxes, and in this sense may be considered their ten-dimensional uplifts. We focus on the supersymmetry equations and Bianchi identities, and find solutions to these that are valid at the two-derivative level and at first order in an expansion parameter which is related to the AdS cosmological constant. This family of solutions is such that the background metric is deformed from the Ricci-flat one to one exhibiting SU(3) × SU(3)-structure, and dilaton gradients and warp factors are induced.
Highlights
That the solutions are not really d-dimensional in any physical sense: physics looks tenor eleven-dimensional to a hypothetical observer
In this work we study ten-dimensional solutions to type IIA string theory of the form AdS4 × X6 which contain orientifold planes and preserve N = 1 supersymmetry
We focus on the supersymmetry equations and Bianchi identities, and find solutions to these that are valid at the twoderivative level and at first order in an expansion parameter which is related to the AdS cosmological constant
Summary
We review the setup considered in [11], and in particular the features that should appear in a 10d description. The approach in [11] performs a 4d analysis of such potential, finding an infinite discretum of N = 1 AdS4 vacua This features of such vacua can be expressed in terms of integrals of 10d gauge invariant field strengths, which in 4d language are seen as specific combinations of flux quanta and axionic scalars [28,29,30]. From these one can build a bispinor Φ± ≡ η+1 ⊗ η±2 †, which can be interpreted as a polyform in the internal space by the Clifford map γm → dxm This form obeys some algebraic constraints, that follow from its definition in terms of spinors, and some differential equations that follow from supersymmetry.
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