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

TL;DR

This paper verifies the AdS/CFT correspondence by computing the partition function of specific N=2 gauge theories on a three-sphere, showing agreement with gravity dual predictions through localization and large-N analysis.

Contribution

It provides the first exact large-N computation of the partition function for non-chiral N=2 quiver Chern-Simons-matter theories on S^3, confirming gravity dual predictions.

Findings

Partition function scales as N^{3/2} in large-N limit.

The computed free energy matches the volume of internal Sasaki-Einstein manifolds.

Results support the AdS/CFT correspondence for these models.

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 $V^{5,2}$.