Three-sphere free energy for classical gauge groups
Author(s)Mezei, Mark Koppany; Pufu, Silviu
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In this note, we calculate the S [superscript 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 , 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.
DepartmentMassachusetts Institute of Technology. Center for Theoretical Physics; Massachusetts Institute of Technology. Department of Physics
Journal of High Energy Physics
Mezei, Mark, and Silviu S. Pufu. “Three-Sphere Free Energy for Classical Gauge Groups.” J. High Energ. Phys. 2014, no. 2 (February 2014).
Final published version