# The F-Theorem and F-Maximization

@article{Pufu2016TheFA,
title={The F-Theorem and F-Maximization},
author={Silviu S. Pufu},
journal={arXiv: High Energy Physics - Theory},
year={2016}
}
• S. Pufu
• Published 9 August 2016
• Physics
• arXiv: High Energy Physics - Theory
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…
50 Citations

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## References

SHOWING 1-10 OF 118 REFERENCES
F-theorem without supersymmetry
• Mathematics
• 2011
The conjectured F-theorem for three-dimensional field theories states that the finite part of the free energy on S3 decreases along RG trajectories and is stationary at the fixed points. In previous
Towards the F-theorem: $\mathcal{N} = 2$ field theories on the three-sphere
• Mathematics, Physics
• 2011
For 3-dimensional field theories with $\mathcal{N} = 2$ supersymmetry the Euclidean path integrals on the three-sphere can be calculated using the method of localization; they reduce to certain
Generalized F-theorem and the ϵ expansion
• Mathematics
• 2015
A bstractSome known constraints on Renormalization Group flow take the form of inequalities: in even dimensions they refer to the coefficient a of the Weyl anomaly, while in odd dimensions to the
Interpolating between a and F
• Mathematics
• 2014
A bstractWe study the dimensional continuation of the sphere free energy in conformal field theories. In continuous dimension d we define the quantity F˜$$\tilde{F}$$ =sin(πd/2) log Z, where Z is
On renormalization group flows and the a-theorem in 6d
• Physics
• 2012
A bstractWe study the extension of the approach to the a-theorem of Komargodski and Schwimmer to quantum field theories in d = 6 spacetime dimensions. The dilaton effective action is obtained up to
From necklace quivers to the F -theorem, operator counting, and T (U(N))
• Mathematics
• 2011
A bstractThe matrix model of Kapustin, Willett, and Yaakov is a powerful tool for exploring the properties of strongly interacting superconformal Chern-Simons theories in 2+1 dimensions. In this
Disk entanglement entropy for a Maxwell field
• Physics
• 2014
In three dimensions, the pure Maxwell theory with compact U(1) gauge group is dual to a free compact scalar, and flows from the Maxwell theory with non-compact gauge group in the ultraviolet to a
Evidence for C-theorems in 6D SCFTs
• Mathematics
• 2015
A bstractUsing the recently established classification of 6D SCFTs we present evidence for the existence of families of weak C-functions, that is, quantities which decrease in a flow from the UV to
A crack in the conformal window
• Physics
• 2013
A bstractIn $\mathcal{N}=2$ 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