Here us a look at the paper that appeared in the arxiv yesterday:
Moduli spaces of Chern-Simons quiver gauge theories (arXiv:0808.0912v1)
First of all let me describe what is quiver gauge theories. There are singularities associated with Dbranes and this is described by quiver gauge theories. Infact quiver is basically a diagram with nodes. The nodes are the unitary U(N) gauge group and the vector multiplets. This connect the nodes representing the U(N) gauge groups and the corresponding vector multiplets. Each link represents a field in bifundamental representation.
The above paper in arxiv looks interesting. Supposedly, the author claim to take the first step toward identifying candidate N=2 conformal Chern Simons quiver gauge theories with ADS4 X Y7 gravity duals.The three dimension Chern Simons gauge theories for N=2 SUSY or higher couple with matter may be ASD4 gauge theory dual. Apparently the simplest vacua of this kind is ADS4 X Y7 where Y7 is the Sasaki- Einstein manifold. The simplest solution are the type of Freund and Rubin soulution that was found for d=11 supergravity (this compactifies S7 (seven sphere) to four dimensional anti de Sitter space.
Interestingly, this is a vacuum of M theory which arises as the dual to the three dimensional conformal field theory of M2 branes in flat space. This also has a Calabi Yau fourfold singularity. In order to find the field theory dual of these kind of solutions one needs to understand the degrees of freedom of these M2 branes. It may be relevant to note that this line of thinking had originally failed because of the no go theorem that says that chiral fermions cannot be given by a smooth manifold. Maldecena et al, showed that the gauge theory duals of a class of ADS4 X S7 background is the N=6 or 8 Chern Simons quivers with certian properties.
In the case of type II string theory, we can construct N = 1 AdS5/CFT4 duals by considering N D3-branes placed at a conical Calabi-Yau 3-fold singularity X. One can also construct gauge theories from string degrees of freedom which sits on a brane. The dual theory is given by N=1 d=4 quiver gauge theory. So if one looks at the vacua of the N=1 d=4 quiver gauge theory, the author tell us that its a symmetric product of Calabi Yau singularity X one started with. Now the gravity dual is ADS5 X Y5 where Y5 is the Einstein Sasaki base of a Calabi Yau cone.
In this paper they look at the classical vacuum moduli space of the Chern Simons gauge theories with arbitrary Chern Simons levels. There could include Coulom branch, Higgs branch or a combination of that. They look at certain branches and look at Chern Simons quiver theories in terms of M2-branes at a CY 4-fold singularity, they believe that this branch should reproduce CY 4-fold as the 1moduli space of the transverse M2-branes. The result is that the vacuum modulis space has a branch which is related to the moduli space of four dimensional N=1 quiver theory.