A crack in the conformal window

Abstract

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(N-c) gauge theory coupled to N-f pairs of fundamental and anti-fundamental superfields in the Veneziano large N-c limit, where x = N-f/N-c is kept fixed. This theory has a superconformal window 1 <= x <= infinity, while for x < 1 supersymmetry is broken. As we reduce x we find “a crack in the superconformal window” - a critical value x(c) approximate to 1.45 where the monopole operators reach the unitarity bound. To continue the theory to x < x(c) we assume that the monopoles become free fields, leading to an accidental global symmetry. Using the Aharony dual description of the theory for x < x(c) allows us to determine the R-charges and F for 1 <= x < x(c). Adding a Chern-Simons term removes the transition at x(c). In these more general theories we study the scaling dimensions of meson operators as functions of x and kappa = vertical bar k vertical bar/N-c. We find that there is an interesting transition in behavior at kappa = 1.