The F-theorem and F-maximization

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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 languageEnglish (US)
Article number443008
JournalJournal of Physics A: Mathematical and Theoretical
Issue number44
StatePublished - Oct 13 2017

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Modeling and Simulation
  • Mathematical Physics
  • General Physics and Astronomy


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


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