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.

We consider N = 2 supergravity in four dimensions, coupled to an arbitrary number of vector-and hypermultiplets, where abelian isometries of the quaternionic hyperscalar target manifold are gauged. Using a static and spherically or hyperbolically symmetric ansatz for the fields, a one-dimensional effective action is derived whose variation yields all the equations of motion. By imposing a sort of Dirac charge quantization condition, one can express the complete scalar potential in terms of a superpotential and write the action as a sum of squares. This leads to first-order flow equations, that imply the second-order equations of motion. The first-order flow turns out to be driven by Hamilton's characteristic function in the Hamilton-Jacobi formalism, and contains among other contributions the superpotential of the scalars. We then include also magnetic gaugings and generalize the flow equations to a symplectically covariant form. Moreover, by rotating the charges in an appropriate way, an alternative set of non-BPS first-order equations is obtained that corresponds to a different squaring of the action. Finally, we use our results to derive the attractor equations for near-horizon geometries of extremal black holes.

We study AdS3$$ \times {S}^3/{\mathrm{\mathbb{Z}}}_k\times {\tilde{S}}^3/{\mathrm{\mathbb{Z}}}_{k^{\prime }} $$ × S 3 / ℤ k × S ˜ 3 / ℤ k ′ solutions to M-theory preserving $$ \mathcal{N} $$ N = (0, 4) supersymmetries, arising as near-horizon limits of M2-M5 brane intersections ending on M5’-branes, with both types of five-branes placed on A-type singularities. Solutions in this class asymptote locally to AdS7$$ /{\mathrm{\mathbb{Z}}}_k\times {\tilde{S}}^3/{\mathrm{\mathbb{Z}}}_{k^{\prime }} $$ / ℤ k × S ˜ 3 / ℤ k ′ , and can thus be interpreted as holographic duals to surface defect CFTs within the $$ \mathcal{N} $$ N = (1, 0) 6d CFT dual to this solution. Upon reduction to Type IIA, we obtain a new class of solutions of the form AdS3× S3/ℤk× S2×Σ2 preserving (0,4) supersymmetries. We construct explicit 2d quiver CFTs dual to these solutions, describing D2-D4 surface defects embedded within the 6d (1,0) quiver CFT dual to the AdS7/ℤk solution to massless IIA. Finally, in the massive case, we show that the recently constructed AdS3× S2× CY2 solutions with $$ \mathcal{N} $$ N = (0, 4) supersymmetries gain a defect interpretation as surface CFTs originating from D2-NS5-D6 defects embedded within the 5d CFT dual to the Brandhuber-Oz AdS6 background.

We present a new BPS flow within minimal N = 1 supergravity in seven dimensions describing a warped AdS 3 background supported by a "dyonic" profile of the three-form. Furthermore, we discuss the holographic interpretation of the above solution in terms of a defect SCFT 2 inside the 6d (1, 0) theory dual to the AdS in the asymptotic region. Finally we provide the brane picture of the aforementioned defect CFT as D2-and wrapped D4-branes ending on a D6 -NS5 -D8 funnel in massive type IIA string theory.

We study several different types of BPS flows within minimal N = 1, D = 7 supergravity with SU(2) gauge group and non-vanishing topological mass. After reviewing some known domain wall solutions involving only the metric and the R + scalar field, we move to considering more general flows involving a "dyonic" profile for the 3-form gauge potential. In this context, we consider flows featuring a Mkw 3 as well as an AdS 3 slicing, write down the corresponding flow equations, and integrate them analytically to obtain many examples of asymptotically AdS 7 solutions in presence of a running 3-form. Furthermore, we move to adding the possibility of non-vanishing vector fields, find the new corresponding flows and integrate them numerically. Finally, we discuss the eleven-dimensional interpretation of the aforementioned solutions as effective descriptions of M2 − M5 bound states.