Abstract
We test the AdS/CFT correspondence by computing the partition function of some \( \mathcal{N} = 2 \) 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 5,2. 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 5,2.
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