Microstates of rotating AdS5 strings

We provide a general formula for the refined topologically twisted index of = 1 gauge theories living on the world -volume of D3-branes at conical Calabi-Yau singularities in the Cardy limit. The index is defined as the partition function on T2 x SW, with a partial topological twist and a Q -deformation along S2, in the presence of background magnetic fluxes and fugacities for the global symmetries and can be used to study the properties of a class of BPS black strings. To this purpose, we find rotating domainwall solutions of five -dimensional gauged supergravity interpolating between AdS5 and a near horizon region consisting of a warped fibration of BTZ over a sphere. We explicitly construct rotating domain -walls that can be embedded in AdS5 x S5 by uplifting a class of four-dimensional rotating black holes. We then provide a microscopic explanation of the entropy of such black holes by using the refined topologically twisted index of A1 = 4 super Yang-Mills.