### Abstract

This contribution contains a review of the role of the three-sphere free energy F in recent developments related to the F-theorem and F-maximization. The F-theorem states that for any Lorentz-invariant RG trajectory connecting a conformal field theory CFT in the ultraviolet to a conformal field theory CFT, the F-coefficient decreases: . I provide many examples of CFTs where one can compute F, approximately or exactly, and discuss various checks of the F-theorem. F-maximization is the principle that in an SCFT, viewed as the deep IR limit of an RG trajectory preserving supersymmetry, the superconformal R-symmetry maximizes F within the set of all R-symmetries preserved by the RG trajectory. I review the derivation of this result and provide examples.

Original language | English (US) |
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Article number | 443008 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 50 |

Issue number | 44 |

DOIs | |

State | Published - Oct 13 2017 |

### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Statistics and Probability
- Modeling and Simulation
- Mathematical Physics
- Physics and Astronomy(all)

### Keywords

- F-maximization
- F-theorem
- Lorentz-invariant
- three-sphere free energy