Three dimensional SCFT from M2 branes at conifold singularities

Recently it was conjectured that parallel branes at conical singularities arerelated to string/M theory on $AdS \times X$ where $X$ is an Einstein manifold.In this paper we consider coincident M2 branes near a conifold singularity whenM theory is compactified on $AdS_4 \times Q^{1,1,1}$ where $Q^{1,1,1} = (SU(2)\times SU(2) \times SU(2))/(U(1) \times U(1))$ is a seven dimensionalSasaki-Einstein manifold. We argue that M theory on $AdS_4 \times Q^{1,1,1}$can be described in terms of a three dimensional superconformal field theory.Weuse the fact that the three dimensional self-mirror duality is preserved byexact marginal operators, as observed by Strassler.Comment: 16 pages, Latex, minor extensions, important references added, acknowledgements extende