We construct families of supersymmetric AdS$_3times Y_7$ and AdS$_3times Y_8$ solutions to type IIB string theory and M-theory, respectively. Here $Y_7$ is an $S^5$ fibration over $Sigma$, while $Y_8$ is an $S^4$ fibration over $Sigma_gtimes Sigma$,
where $Sigma_g$ is a Riemann surface of genus $g>1$ and $Sigma$ is a two-dimensional orbifold known as a spindle. We interpret the solutions as near-horizon limits of $N$ D3-branes wrapped on $Sigma$ and $N$ M5-branes wrapped on $Sigma_gtimes Sigma$, 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 study solutions in the Plebanski--Demianski family which describe an accelerating, rotating and dyonically charged black hole in $AdS_4$. These are solutions of $D=4$ Einstein-Maxwell theory with a negative cosmological constant and hence minimal
$D=4$ gauged supergravity. It is well known that when the acceleration is non-vanishing the $D=4$ black hole metrics have conical singularities. By uplifting the solutions to $D=11$ supergravity using a regular Sasaki-Einstein $7$-manifold, $SE_7$, we show how the free parameters can be chosen to eliminate the conical singularities. Topologically, the $D=11$ solutions incorporate an $SE_7$ fibration over a two-dimensional weighted projective space, $mathbb{WCP}^1_{[n_-,n_+]}$, also known as a spindle, which is labelled by two integers that determine the conical singularities of the $D=4$ metrics. We also discuss the supersymmetric and extremal limit and show that the near horizon limit gives rise to a new family of regular supersymmetric $AdS_2times Y_9$ solutions of $D=11$ supergravity, which generalise a known family by the addition of a rotation parameter. We calculate the entropy of these black holes and argue that it should be possible to derive this from certain ${cal N}=2$, $d=3$ quiver gauge theories compactified on a spinning spindle with appropriate magnetic flux.
We construct supersymmetric $AdS_3times Sigma$ solutions of minimal gauged supergravity in $D=5$, where $Sigma$ is a two-dimensional orbifold known as a spindle. Remarkably, these uplift on $S^5$, or more generally on any regular Sasaki-Einstein mani
fold, to smooth solutions of type IIB supergravity. The solutions are dual to $d=2$, $mathcal{N}=(0,2)$ SCFTs and we show that the central charge for the gravity solution agrees with a field theory calculation associated with D3-branes wrapped on $Sigma$. Unlike for smooth $Sigma$ the superconformal R-symmetry mixes with the $U(1)$ isometry of the spindle.
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 reno
rmalized 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.
