In this note, we calculate the S3 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 , which we extend to next-to-leading order in 1/N. The second method generalizes the Fermi gas approach of  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.
All Science Journal Classification (ASJC) codes
- Nuclear and High Energy Physics
- AdS-CFT Correspondence
- Extended Supersymmetry
- Matrix Models
- Supersymmetric gauge theory