D4-branes wrapped on a spindle

We construct supersymmetric AdS_4xSigma solutions of D=6 gauged supergravity, where Sigma is a two-dimensional orbifold known as a spindle. These uplift to solutions of massive type IIA supergravity using a general prescription, that we describe. We argue that these solutions correspond to the near-horizon limit of a system of N_f D8-branes, together with N D4-branes wrapped on a spindle, embedded as a holomorphic curve inside a Calabi-Yau three-fold. The dual field theories are d=3, N = 2 SCFTs that arise from a twisted compactification of the d=5, N=1 USp(2N) gauge theory. We show that the holographic free energy associated to these solutions is reproduced by extremizing an off-shell free energy, that we conjecture to arise in the large N limit of the localized partition function of the d=5 theories on S^3xSigma. We formulate a universal proposal for a class of off-shell free energies, whose extremization reproduces all previous results for branes wrapped on spindles, as well as on genus g Riemann surfaces Sigma_g. We further illustrate this proposal discussing D4-branes wrapped on SigmaxSigma_g, for which we present a supersymmetric AdS_2xSigmaxSigma_g solution of D=6 gauged supergravity along with the associated entropy function.