We construct supersymmetric AdS 5 × Σ solutions of D = 7 gauged supergravity, where Σ is a two-dimensional orbifold known as a spindle. These uplift on S 4 to solutions of D = 11 supergravity which have orbifold singularites. We argue that the solutions are dual to d = 4, N = 1 SCFTs that arise from N M5-branes wrapped on a spindle, embedded as a holomorphic curve inside a Calabi-Yau three-fold. In contrast to the usual topological twist solutions, the superconformal R-symmetry mixes with the isometry of the spindle in the IR, and we verify this via a field theory calculation, as well as reproducing the gravity formula for the central charge.

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We construct families of supersymmetric AdS3 × Y7 and AdS3 × Y8 solutions to type IIB string theory and M-theory, respectively. Here Y7 is an S5 fibration over Σ, while Y8 is an S4 fibration over Σg × Σ, where Σg is a Riemann surface of genus g > 1 and Σ is a two-dimensional orbifold known as a spindle. We interpret the solutions as near-horizon limits of N D3-branes wrapped on Σ and N M5-branes wrapped on Σg × Σ, respectively. These are holographically dual to d = 2, (0, 2) SCFTs, and we show that the central charge and superconformal R-symmetry of the gravity solutions agree with dual field theory calculations.

We derive a simple formula for the action of any supersymmetric solution to minimal gauged supergravity in the AdS 4 /CFT 3 correspondence. Such solutions are equipped with a supersymmetric Killing vector, and we show that the holographically renormalized action may be expressed entirely in terms of the weights of this vector field at its fixed points, together with certain topological data. In this sense, the classical gravitational partition function localizes in the bulk. We illustrate our general formula with a number of explicit examples, in which exact dual field theory computations are also available, which include supersymmetric Taub-NUT and Taub-bolt type spacetimes, as well as black hole solutions. Our simple topological formula also allows us to write down the action of any solution, provided it exists.

We study a spontaneously broken SUð2Þ Chern-Simons-Higgs model coupled though a Higgs portal to an uncharged triplet scalar with a vacuum state competing with the Higgs one. We find vortexlike solutions to the field equations in different parameter space regions. Depending on the scalar coupling constants, we find a parameter region in which the competing order creates a halo about the Chern-Simons-Higgs vortex core, together with two other regions, one where no vortex solutions exist and the other where ordinary Chern-Simons-Higgs vortices can be found. We derive the low-energy theory for the moduli fields on the vortex world sheet and also discuss the connection of our results with those found in studies of competing orders in high-temperature superconductors.