## Advances in Theoretical and Mathematical Physics

- Adv. Theor. Math. Phys.
- Volume 18, Number 1 (2014), 129-175.

### Superconformal indices, Sasaki-Einstein manifolds, and cyclic homologies

Richard Eager, Johannes Schmude, and Yuji Tachikawa

#### Abstract

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

#### Article information

**Source**

Adv. Theor. Math. Phys., Volume 18, Number 1 (2014), 129-175.

**Dates**

First available in Project Euclid: 10 October 2014

**Permanent link to this document**

https://projecteuclid.org/euclid.atmp/1412953899

**Mathematical Reviews number (MathSciNet)**

MR3268235

**Zentralblatt MATH identifier**

1309.81242

#### Citation

Eager, Richard; Schmude, Johannes; Tachikawa, Yuji. Superconformal indices, Sasaki-Einstein manifolds, and cyclic homologies. Adv. Theor. Math. Phys. 18 (2014), no. 1, 129--175. https://projecteuclid.org/euclid.atmp/1412953899