Holographic interpolation between a and F

A bstract An interpolating function F ˜ between the a -anomaly coefficient in even dimensions and the free energy on an odd-dimensional sphere has been proposed recently and is conjectured to monotonically decrease along any renormalization group flow in continuous dimension d . We examine F ˜ in th...

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Bibliographic Details
Published inThe journal of high energy physics Vol. 2014; no. 12; p. 1
Main Authors Kawano, Teruhiko, Nakaguchi, Yuki, Nishioka, Tatsuma
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.12.2014
Springer Nature B.V
Subjects
Classical and Quantum Gravitation
Elementary Particles
High energy physics
Physics
Physics and Astronomy
Quantum Field Theories
Quantum Field Theory
Quantum Physics
Regular Article - Theoretical Physics
Relativity Theory
String Theory
AdS-CFT Correspondence
Renormalization Group
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Summary:A bstract An interpolating function F ˜ between the a -anomaly coefficient in even dimensions and the free energy on an odd-dimensional sphere has been proposed recently and is conjectured to monotonically decrease along any renormalization group flow in continuous dimension d . We examine F ˜ in the large- N CFT’s in d dimensions holographically described by the Einstein-Hilbert gravity in the AdS d +1 space. We show that F ˜ is a smooth function of d and correctly interpolates the a coefficients and the free energies. The monotonicity of F ˜ along an RG flow follows from the analytic continuation of the holographic c -theorem to continuous d , which completes the proof of the conjecture.
ISSN:1029-8479
1029-8479
DOI:10.1007/JHEP12(2014)161