Microstates of rotating AdS5 strings

We provide a general formula for the refined topologically twisted index of N = 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×Sω2, with a partial topological twist and a Ω-deformation along S , 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 domain- wall 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× 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 N = 4 super Yang-Mills.