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.
All Science Journal Classification (ASJC) codes
- Nuclear and High Energy Physics
- Chern-simons theories
- Field theories in lower dimensions
- Matrix models
- Supersymmetry and duality