D4-branes wrapped on a spindle

Abstract

Abstract We construct supersymmetric "Image missing"solutions of D = 6 gauged supergravity, where "Image missing" 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 Nf 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, $$ \mathcal{N} $$ N = 2 SCFTs that arise from a twisted compactification of the d = 5, $$ \mathcal{N} $$ 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 "Image missing". 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 Σg. We further illustrate this proposal discussing D4-branes wrapped on "Image missing", for which we present a supersymmetric "Image missing" solution of D = 6 gauged supergravity along with the associated entropy function.