Holographic RG flows on curved manifolds and the F-theorem
Abstract We study F-functions in the context of field theories on S 3 using gauge-gravity duality, with the radius of S 3 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 mono...
Main Authors: | , , , |
---|---|
Format: | Article |
Language: | English |
Published: |
SpringerOpen
2019-02-01
|
Series: | Journal of High Energy Physics |
Subjects: | |
Online Access: | http://link.springer.com/article/10.1007/JHEP02(2019)055 |
id |
doaj-6b2206a34eb24d91b301b3da42afb834 |
---|---|
record_format |
Article |
spelling |
doaj-6b2206a34eb24d91b301b3da42afb8342020-11-25T01:21:50ZengSpringerOpenJournal of High Energy Physics1029-84792019-02-012019218610.1007/JHEP02(2019)055Holographic RG flows on curved manifolds and the F-theoremJ. K. Ghosh0E. Kiritsis1F. Nitti2L. T. Witkowski3APC, AstroParticule et Cosmologie, Université Paris Diderot, CNRS/IN2P3, CEA/IRFU, Observatoire de Paris, Sorbonne Paris CitéAPC, AstroParticule et Cosmologie, Université Paris Diderot, CNRS/IN2P3, CEA/IRFU, Observatoire de Paris, Sorbonne Paris CitéAPC, AstroParticule et Cosmologie, Université Paris Diderot, CNRS/IN2P3, CEA/IRFU, Observatoire de Paris, Sorbonne Paris CitéAPC, AstroParticule et Cosmologie, Université Paris Diderot, CNRS/IN2P3, CEA/IRFU, Observatoire de Paris, Sorbonne Paris CitéAbstract We study F-functions in the context of field theories on S 3 using gauge-gravity duality, with the radius of S 3 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 S 3 (Δ = 2) and the free boson on S 3 (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.http://link.springer.com/article/10.1007/JHEP02(2019)055AdS-CFT CorrespondenceRenormalization Group |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
J. K. Ghosh E. Kiritsis F. Nitti L. T. Witkowski |
spellingShingle |
J. K. Ghosh E. Kiritsis F. Nitti L. T. Witkowski Holographic RG flows on curved manifolds and the F-theorem Journal of High Energy Physics AdS-CFT Correspondence Renormalization Group |
author_facet |
J. K. Ghosh E. Kiritsis F. Nitti L. T. Witkowski |
author_sort |
J. K. Ghosh |
title |
Holographic RG flows on curved manifolds and the F-theorem |
title_short |
Holographic RG flows on curved manifolds and the F-theorem |
title_full |
Holographic RG flows on curved manifolds and the F-theorem |
title_fullStr |
Holographic RG flows on curved manifolds and the F-theorem |
title_full_unstemmed |
Holographic RG flows on curved manifolds and the F-theorem |
title_sort |
holographic rg flows on curved manifolds and the f-theorem |
publisher |
SpringerOpen |
series |
Journal of High Energy Physics |
issn |
1029-8479 |
publishDate |
2019-02-01 |
description |
Abstract We study F-functions in the context of field theories on S 3 using gauge-gravity duality, with the radius of S 3 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 S 3 (Δ = 2) and the free boson on S 3 (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. |
topic |
AdS-CFT Correspondence Renormalization Group |
url |
http://link.springer.com/article/10.1007/JHEP02(2019)055 |
work_keys_str_mv |
AT jkghosh holographicrgflowsoncurvedmanifoldsandtheftheorem AT ekiritsis holographicrgflowsoncurvedmanifoldsandtheftheorem AT fnitti holographicrgflowsoncurvedmanifoldsandtheftheorem AT ltwitkowski holographicrgflowsoncurvedmanifoldsandtheftheorem |
_version_ |
1725128989254615040 |