### 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 ≤ ∞, while for x < 1 supersymmetry is broken. As we reduce x we find “a crack in the superconformal window” — a critical value x_{c} ≈ 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 κ = |k| /N_{c}. We find that there is an interesting transition in behavior at κ = 1.

Original language | English (US) |
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Article number | 165 |

Journal | Journal of High Energy Physics |

Volume | 2013 |

Issue number | 4 |

DOIs | |

State | Published - Apr 30 2013 |

### All Science Journal Classification (ASJC) codes

- Nuclear and High Energy Physics

### Keywords

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

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## Cite this

*Journal of High Energy Physics*,

*2013*(4), [165]. https://doi.org/10.1007/JHEP04(2013)165