From necklace quivers to the F-theorem, operator counting, and T (U(N))

Daniel R. Gulotta, Christopher P. Herzog, Silviu S. Pufu

Research output: Contribution to journalArticlepeer-review

61 Scopus citations


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 S3 . 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 S3.

Original languageEnglish (US)
Article number77
JournalJournal of High Energy Physics
Issue number12
StatePublished - 2011

All Science Journal Classification (ASJC) codes

  • Nuclear and High Energy Physics


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


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