A crack in the conformal window

Benjamin R. Safdi, Igor R. Klebanov, Jeongseog Lee

Research output: Contribution to journalArticlepeer-review

30 Scopus citations


In N = 2 superconformal three-dimensional field theory the R-symmetry is determined by locally maximizing the free energy F on the three-sphere. Using F-maximization, we study the N = 2 supersymmetric U(Nc) gauge theory coupled to Nf pairs of fundamental and anti-fundamental superfields in the Veneziano large Nc limit, where x = Nf /Nc is kept fixed. This theory has a superconformal window 1 ≤ x ≤ ∞, while for x < 1 supersymmetry is broken. As we reduce x we find “a crack in the superconformal window” — a critical value xc ≈ 1.45 where the monopole operators reach the unitarity bound. To continue the theory to x < xc we assume that the monopoles become free fields, leading to an accidental global symmetry. Using the Aharony dual description of the theory for x < xc allows us to determine the R-charges and F for 1 ≤ x < xc. Adding a Chern-Simons term removes the transition at xc . In these more general theories we study the scaling dimensions of meson operators as functions of x and κ = |k| /Nc. We find that there is an interesting transition in behavior at κ = 1.

Original languageEnglish (US)
Article number165
JournalJournal of High Energy Physics
Issue number4
StatePublished - Apr 30 2013

All Science Journal Classification (ASJC) codes

  • Nuclear and High Energy Physics


  • Chern-simons theories
  • Field theories in lower dimensions
  • Matrix models
  • Supersymmetry and duality


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