Abstract
We classify Minkowski4 solutions in type IIA supergravity, with mathcal{N} = 2 supersymmetry and an SU(2) R-symmetry of a certain type. Many subcases can be reduced to relatively simple PDEs, among which we recover various intersecting brane systems, and AdSd solutions, d = 5, 6, 7, and in particular the recently found general massive AdS7 solutions. Imposing compactness of the internal six-manifold we obtain promising solutions with localized D-branes and O-planes.
Highlights
String theory compactifications become harder to find as the cosmological constant of the spacetime factor increases
Many subcases can be reduced to relatively simple PDEs, among which we recover various intersecting brane systems, and AdSd solutions, d = 5, 6, 7, and in particular the recently found general massive AdS7 solutions
There are many known families of AdS examples (Λ < 0); the oldest known type is the Freund-Rubin class [1] which has a Sasaki-Einstein as internal space, but many other possibilities have been found over the years
Summary
String theory compactifications become harder to find as the cosmological constant of the spacetime factor increases. This can succeed because, in some situations, there are enough internal spinors so that their bilinears can define an entire vielbein (in this context, an “identity structure”) While this phenomenon has been known for a long time, it has become clearer in recent times that the local metrics naturally chosen by supersymmetry often tend to have automatically the correct behaviors one would expect from O-planes and D-branes. Within each, preserved supersymmetry can be reduced to a system of PDEs; sometimes further sub-subclasses suggest themselves, and within each the PDEs simplify considerably Some of these systems have appeared earlier in the literature for intersecting brane solutions [25,26,27]. While this work was being completed, [28] appeared, which has some overlap with our section 5.2 about recovering AdS7 solutions
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