Superconformal Indices and M2-Branes

TL;DR

This paper computes the superconformal index for M2-branes on Sasaki-Einstein manifolds, linking supergravity and gauge theory results, and derives the spectrum of Kaluza-Klein multiplets.

Contribution

It provides a general formula for the superconformal index on arbitrary Sasaki-Einstein seven-manifolds and matches supergravity with gauge theory results.

Findings

Derived the superconformal index in terms of cohomology groups.

Matched supergravity results with gauge theory calculations.

Determined the spectrum of short Kaluza-Klein multiplets.

Abstract

We derive the superconformal index of the world-volume theory on M2-branes probing the cone over an arbitrary Sasaki-Einstein seven-manifold. The index is expressed in terms of the cohomology groups of the cone. We match our supergravity results with known results from gauge theory. Along the way we derive the spectrum of short Kaluza-Klein multiplets on generic Sasaki-Einstein seven-manifolds.