### Abstract

In this note, we calculate the S^{3} free energy F of 3-d N ≥ 4 supersymmetric gauge theories with U(N), O(N), and USp(2N) gauge groups and matter hypermultiplets in the fundamental and two-index tensor representations. Supersymmetric localization reduces the computation of F to a matrix model that we solve in the large N limit using two different methods. The first method is a saddle point approximation first introduced in [1], which we extend to next-to-leading order in 1/N. The second method generalizes the Fermi gas approach of [2] to theories with symplectic and orthogonal gauge groups, and yields an expression for F valid to all orders in 1/N. In developing the second method, we use a non-trivial generalization of the Cauchy determinant formula.

Original language | English (US) |
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Article number | 37 |

Journal | Journal of High Energy Physics |

Volume | 2014 |

Issue number | 2 |

DOIs | |

State | Published - Feb 2014 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Nuclear and High Energy Physics

### Keywords

- AdS-CFT Correspondence
- Extended Supersymmetry
- Matrix Models
- Supersymmetric gauge theory

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## Cite this

*Journal of High Energy Physics*,

*2014*(2), [37]. https://doi.org/10.1007/JHEP02(2014)037