M5 branes wrapping $\mathbb{WCP}^2$ and spindles fibred over constant curvature Riemann surfaces

Abstract

We classify AdS$_3$ solutions of the U(1) invariant sector of minimal $d=7$ supergravity. We find two classes of solutions preserving ${\cal N}=(2,0)$ supersymmetry for which the internal space M$_4$ is either a negative curvature Kahler-Einstein manifold or a circle fibration over $\Sigma\times \mathbb{R}$. For the later, in the case that $\Sigma$ has constant curvature, we reduce finding a solution to solving a single ODE that admits polynomial solutions. Among these are interesting solutions whose uplifts to $d=11$ describe M5 branes wrapping various $d=4$ orbifolds. These include a topological $\mathbb{CP}^2$ with 2 orbifold fixed points that we identify as the weighted projective space $\mathbb{WCP}^2_{[k,k,\ell]}$. We are also able to construct solutions with M5 branes that wrap a spindle fibred over constant curvature Riemann surfaces of arbitrary genus. Such solutions should provide holographic duals to the ${\cal N}=(2,0)$ SCFT associated to the M5 brane compactified to $d=2$ on these orbifolds. We match the holographic central charges of these solutions to a field theory computation in terms of anomaly polynomials and c-extremisation.