### Abstract

The matrix model of Kapustin, Willett, and Yaakov is a powerful tool for exploring the properties of strongly interacting superconformal Chern-Simons theories in 2+1 dimensions. In this paper, we use this matrix model to study necklace quiver gauge theories with N = 3 supersymmetry and U(N)^{d} gauge groups in the limit of large N. In its simplest application, the matrix model computes the free energy of the gauge theory on S^{3} . The conjectured F-theorem states that this quantity should decrease under renormalization group ow. We show that for a simple class of such ows, the F-theorem holds for our necklace theories. We also provide a relationship between matrix model eigenvalue distributions and numbers of chiral operators that we conjecture holds more generally. Through the AdS/CFT correspondence, there is therefore a natural dual geometric interpretation of the matrix model saddle point in terms of volumes of 7-d tri-Sasaki Einstein spaces and some of their 5-d submanifolds. As a final bonus, our analysis gives us the partition function of the T(U(N)) theory on S^{3}.

Original language | English (US) |
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Article number | 77 |

Journal | Journal of High Energy Physics |

Volume | 2011 |

Issue number | 12 |

DOIs | |

State | Published - Dec 29 2011 |

### All Science Journal Classification (ASJC) codes

- Nuclear and High Energy Physics

### Keywords

- 1/N Expansion
- AdS-CFT Correspondence
- Chern-Simons Theories
- Strong Coupling Expansion

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## Cite this

*Journal of High Energy Physics*,

*2011*(12), [77]. https://doi.org/10.1007/JHEP12(2011)077