  We calculate the superconformal Witten index for the Chern-Simons-matter
theory which was proposed to describe multiple M2-branes on $C^2 X C^2/Z_k$. We
consider a variant of this model, which exhibits explicit N=3 supersymmetry and
has the advantage of not having an exotic branch of the moduli space. At $k=1$,
we compare the index with that from the proposed gravity dual and find a
disagreement.
