Journal of High Energy Physics

, 2011:77 | Cite as

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

  • Daniel R. Gulotta
  • Christopher P. Herzog
  • Silviu S. PufuEmail author


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 \( \mathcal{N} = {3} \) 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 S 3. The conjectured F -theorem states that this quantity should decrease under renormalization group flow. We show that for a simple class of such flows, 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 S 3.


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


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Copyright information

© SISSA, Trieste, Italy 2011

Authors and Affiliations

  • Daniel R. Gulotta
    • 1
  • Christopher P. Herzog
    • 1
  • Silviu S. Pufu
    • 1
    Email author
  1. 1.Joseph Henry Laboratories, Princeton UniversityPrincetonUSA

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