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The superconformal index of the quiver gauge theory dual to type IIB stringtheory on the product of an arbitrary smooth Sasaki-Einstein manifold withfive-dimensional AdS space is calculated both from the gauge theory and gravityviewpoints. We find complete agreement. Along the way, we find that the indexon the gravity side can be expressed in terms of the Kohn-Rossi cohomology ofthe Sasaki-Einstein manifold and that the index of a quiver gauge theory equalsthe Euler characteristic of the cyclic homology of the Ginzburg dg algebraassociated to the quiver.

Superconformal Indices, Sasaki-Einstein Manifolds, and Cyclic Homologies