Calculating the partition function of N=2 gauge theories on S3 and AdS/CFT correspondence

We test the AdS/CFT correspondence by computing the partition function of some N = 2 quiver Chern-Simons-matter theories on three-sphere. The M-theory backgrounds are of the Freund-Rubin type with the seven-dimensional internal space given as Sasaki-Einstein manifolds Q(1,1,1) or V-5,V-2. Localization technique reduces the exact path integral to a matrix model, and we study the large-N behavior of the partition function. For simplicity we consider only non-chiral models which have a real-valued partition function. The result is in full agreement with the prediction of the gravity duals, i.e. the free energy is proportional to N-3/2 and the coefficient matches correctly the volume of Q(1,1,1) and V-5,V-2.