D4-branes wrapped on a spindle

We construct supersymmetric AdS(4)x Sigma 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-3 x Sigma. 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 Sigma x Sigma(g), for which we present a supersymmetric AdS2 x Sigma x Sigma(g) solution of D = 6 gauged supergravity along with the associated entropy function.

Automated summary

We construct supersymmetric AdS(4)x Sigma solutions of D = 6 gauged supergravity, and uplift them to massive type IIA supergravity solutions using a general prescription. These solutions correspond to a system of D8-branes and D4-branes wrapped on a spindle, embedded in a Calabi-Yau three-fold. The dual field theories are d = 3, N = 2 SCFTs arising from a twisted compactification of the d = 5, N = 1 USp(2N) gauge theory.