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arXiv · 1102.5565

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

Sangmo Cheon·Hyojoong Kim·Nakwoo Kim
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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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Sangmo Cheon, Hyojoong Kim, Nakwoo Kim. 2011-02-28. Calculating the partition function of N=2 Gauge theories on $S^3$ and AdS/CFT correspondence. https://doi.org/10.1007/jhep05(2011)134

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