Reduced Chern-Simons quiver theories and cohomological 3-algebra models

We study the BPS spectrum and vacuum moduli spaces in dimensional reductions of Chern-Simons-matter theories with N >= 2 supersymmetry to zero dimensions. Our main example is a matrix model version of the ABJM theory that we relate explicitly to certain reduced 3-algebra models. We find the explicit maps from Chern-Simons quiver matrix models to dual IKKT matrix models. We address the problem of topologically twisting the ABJM matrix model, and along the way construct a new twist of the IKKT model. We construct a cohomological matrix model whose partition function localizes onto a moduli space specified by 3-algebra relations that live in the double of the conifold quiver. It computes an equivariant index enumerating framed BPS states with specified R-charges that can be expressed as a combinatorial sum over certain filtered pyramid partitions.