Three-sphere free energy for classical gauge groups

Márk Mezei, Silviu S. Pufu

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52 Scopus citations


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 [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 languageEnglish (US)
Article number37
JournalJournal of High Energy Physics
Issue number2
StatePublished - Feb 2014
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Nuclear and High Energy Physics


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


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