Among the possible superalgebras that contain the AdS 3 isometries, two interesting possibilities are the exceptional F (4) and G(3). Their R-symmetry is respectively SO(7) and G 2 , and the amount of supersymmetry N = 8 and N = 7. We find that there exist two (locally) unique solutions in type IIA supergravity that realize these superalgebras, and we provide their analytic expressions. In both cases, the internal space is obtained by a round six-sphere fibred over an interval, with an O8-plane at one end. The R-symmetry is the symmetry group of the sphere; in the G(3) case, it is broken to G 2 by fluxes. We also find several numerical N = 1 solutions with G 2 flavor symmetry, with various localized sources, including O2-planes and O8-planes.The ORCID identification number(s) for the author(s) of this article can be found under https://doi.org/10.1002/prop.2018000601 The recent work [9] found that these are allowed superalgebras for an AdS 3 solution; see Table 2 there. In older work, superconformal algebras in two dimensions associated with F (4) and G(3) were found and studied, [10][11][12] confirming this possibility from the dual CFT point of view.
AdS 7 supersymmetric solutions in type IIA have been classified, and they are infinitely many. Moreover, every such solution has a non-supersymmetric sister. In this paper, we study the perturbative and non-perturbative stability of these non-supersymmetric solutions, focusing on cases without orientifolds. Perturbatively, we first look at the KK spectrum of spin-2 excitations. This does not exhibit instabilities, but it does show that there is no separation of scales for either the BPS and the non-BPS case, thus proving for supersymmetric AdS 7 a well-known recent conjecture. We then use 7d gauged supergravity and a brane polarization computation to access part of the spectrum of KK scalars. The result signals an instability for all non-supersymmetric solutions except those that have a single D8 on each side. We finally look at non-perturbative instabilities, and find that NS5 bubbles make these remaining solutions decay.
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