A Crack in the Conformal Window

TL;DR

This paper investigates the superconformal window of 3D N=2 supersymmetric gauge theories, identifying a critical point where monopole operators become free, and explores how adding Chern-Simons terms affects this transition.

Contribution

It uncovers a critical value in the superconformal window where monopoles reach the unitarity bound and analyzes the effects of Chern-Simons terms on this transition.

Findings

Identification of a critical x_c ≈ 1.45 where monopoles become free

Use of Aharony duality to determine R-charges below x_c

Chern-Simons terms remove the transition at x_c

Abstract

In {\cal 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 {\cal 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 \leq x \leq \infty, while for x < 1 supersymmetry is broken. As we reduce x we find "a crack in the superconformal window" - a critical value x_c \approx 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 \leq 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 = |k| / N_c. We find that there is an interesting transition in behavior at \kappa = 1.