The F-Theorem and F-Maximization

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_UV in the ultraviolet to a conformal field theory CFT_IR, the F-coefficient decreases: F_UV > F_IR. 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 N=2 SCFT, viewed as the deep IR limit of an RG trajectory preserving N=2 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.

This is a contribution to the review volume `Localization techniques in quantum field theories' (eds. V. Pestun and M. Zabzine) which contains 17 Chapters. The complete volume is summarized in arXiv:1608.02952 and it can be downloaded at https://arxiv.org/src/1608.02952/anc/LocQFT.pdf or http://pestun.ihes.fr/pages/LocalizationReview/LocQFT.pdf

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• Holographic Entanglement Entropy in Cutoff AdS
• Curious Aspects of Three-Dimensional $\mathcal{N}=1$ SCFTs
• Comments on Squashed-sphere Partition Functions
• Mass Deformations of the ABJM Theory: The Holographic Free Energy
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• Wilsonian Effective Action and Entanglement Entropy
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• The 3d $A$-model and generalised symmetries, Part I: bosonic Chern-Simons theories
• The Holographic Contributions to the Sphere Free Energy
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