Journal of High Energy Physics

, 2019:55 | Cite as

Holographic RG flows on curved manifolds and the F-theorem

  • J. K. Ghosh
  • E. Kiritsis
  • F. Nitti
  • L. T. WitkowskiEmail author
Open Access
Regular Article - Theoretical Physics


We study F-functions in the context of field theories on S3 using gauge-gravity duality, with the radius of S3 playing the role of RG scale. We show that the on-shell action, evaluated over a set of holographic RG flow solutions, can be used to define good F-functions, which decrease monotonically along the RG flow from the UV to the IR for a wide range of examples. If the operator perturbing the UV CFT has dimension Δ > 3/2 these F -functions correspond to an appropriately renormalized free energy. If instead the perturbing operator has dimension Δ < 3/2 it is the quantum effective potential, i.e. the Legendre transform of the free energy, which gives rise to good F-functions. We check that these observations hold beyond holography for the case of a free fermion on S3 (Δ = 2) and the free boson on S3 (Δ = 1), resolving a long-standing problem regarding the non-monotonicity of the free energy for the free massive scalar. We also show that for a particular choice of entangling surface, we can define good F-functions from an entanglement entropy, which coincide with certain F-functions obtained from the on-shell action.


AdS-CFT Correspondence Renormalization Group 


Open Access

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Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.APC, AstroParticule et Cosmologie, Université Paris Diderot, CNRS/IN2P3, CEA/IRFU, Observatoire de Paris, Sorbonne Paris CitéParis Cedex 13France
  2. 2.Crete Center for Theoretical Physics, Department of PhysicsUniversity of CreteHeraklionGreece

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