Holographic RG flows on curved manifolds and the F-theorem

被引：0
作者：
J. K. Ghosh
E. Kiritsis
F. Nitti
L. T. Witkowski
机构：
[1] APC,Crete Center for Theoretical Physics, Department of Physics
[2] AstroParticule et Cosmologie,undefined
[3] Université Paris Diderot,undefined
[4] CNRS/IN2P3,undefined
[5] CEA/IRFU,undefined
[6] Observatoire de Paris,undefined
[7] Sorbonne Paris Cité,undefined
[8] University of Crete,undefined
来源：
Journal of High Energy Physics | / 2019卷
关键词：
AdS-CFT Correspondence; Renormalization Group;
D O I：
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摘要：
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.
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