Cyclic homology and the superconformal index

The superconformal index of many interesting superconformal field theories can be computed using the index of a weakly coupled quiver gauge theory. I will explain how the superconformal index can naturally be interpreted in terms of the cyclic homology of the Ginzburg DG algebra associated to the quiver gauge theory. If the quiver gauge theory has a holographic dual description, then we will see that the superconformal index of the gauge theory and its dual gravitational description agree. The proof makes crucial use of the invariance of cyclic homology under derived equivalence.