# AdS/QCD, Light-Front Holography, and the Non- perturbative Running Coupling

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Referee this paper: arXiv:1002.4660

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This 2010 paper by S.J. Brodsky, G.F. de Teramond and A. Deur shows that the combination of Anti-de Sitter space (AdS) methods with light-front (LF) holography provides a remarkably accurate first approximation for the spectra and wavefunctions of meson and baryon light-quark bound states.

''The resulting bound-state Hamiltonian equation of motion in QCD leads to relativistic light-front wave equations in terms of an invariant impact variable ζ which measures the separation of the quark and gluonic constituents within the hadron at equal light-front time. These equations of motion in physical space-time are equivalent to the equations of motion which describe the propagation of spin-J modes in anti-de Sitter (AdS) space. The eigenvalues give the hadronic spectrum, and the eigenmodes represent the probability distributions of the hadronic constituents at a given scale. A positive-sign confining dilaton background modifying AdS space gives a very good account of meson and baryon spectroscopy and form factors. The light-front holographic mapping of this model also leads to a non-perturbative effective coupling $α_s^{AdS}(Q^2)$ which agrees with the effective charge defined by the Bjorken sum rule and lattice simulations. It displays a transition from perturbative to nonperturbative conformal regimes at a momentum scale ∼1 GeV. The resulting β-function appears to capture the essential characteristics of the full β-function of QCD, thus giving further support to the application of the gauge/gravity duality to the confining dynamics of strongly coupled QCD.''

summarized
paper authored Feb 24, 2010 to hep-th
recategorized Aug 27, 2014

I read in the introduction: "The AdS/CFT duality provides a gravity description in a (d+ 1)-dimensional AdS space-time in terms of a at d-dimensional conformally-invariant quantum field theory defined at the AdS asymptotic boundary. Thus, in principle, one can compute physical observables in a strongly coupled gauge theory in terms of a classical gravity theory."

I think there may not be any "thus" nor "in principle" here. CFT and QCD are different things. I do not see any logic in their statement, even though later on they deform something and use approximations for other things in order to apply some tools. The statement itself must be "deformed", IMHO.

@VladimirKalitvianski you seem not to be familiar enough with the topics of the paper at a technical level. If you have questions about the basics of  AdS/CFT, holography, etc please ask them in the Q&A part (if they are on topic for PhysicsOverflow). The comments in the Reviews section are not intended to clarify basic mis/non-understandings of readers but for people, who are sufficiently knowledgeable about the topics at hand, to discuss the paper at research-level.

@VladimirKalitvianski : in your citation, the "thus" is justified because the "d-dimensional conformally-invariant boundary defined at the AdS asymptotic boundary" is indeed "a strongly coupled gauge theory". Of course, this theory is not pure QCD, what you cite does not claim that it is (the statement is  logically correct), and if one wants to deduce something on a QCD like theory, one has to work (and it is the subject of the paper).

@40227: Thanks, I did not know it.

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