Regular Seminar Daisuke Yokoyama (King's College London)
We study the free energy of the three dimensional N=2 supersymmetric Chern-Simons-Matter theory dual to AdS4 times toric seven dimensional Sasaki-Einstein manifold. Although it is not known in general how to construct the CSM theory from the geometric data of the 7d SE manifold (which is called toric diagram), the free energy in the large N limit may be derived. We present the free energy as a quartic polynomial of trial R-charges for generic toric diagram with up to 6 vertices, and some particular diagrams with 8 vertices. The free energy reproduces the Martelli-Sparks-Yau volume function.