Calculating the partition function of N=2 Gauge theories on $S^3$ and AdS/CFT correspondence

Details Calculating the partition function of N=2 Gauge theories on $S^3$ and AdS/CFT correspondence Calculating the partition function of N=2 Gauge theories on $S^3$ and AdS/CFT correspondence

2011-02-28

arxiv.org/abs/1102.5565v3

Physics

High Energy Physics

High Energy Physics - Theory

v2. minor revision;v3. clarification on Z extremization, 23 pages, 9 figures

Scientific paper

We test the AdS/CFT correspondence by computing the partition function of some $\cN=2$ 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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