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Title: ADS/CFT and QCD

Abstract

The AdS/CFT correspondence between string theory in AdS space and conformal .eld theories in physical spacetime leads to an analytic, semi-classical model for strongly-coupled QCD which has scale invariance and dimensional counting at short distances and color confinement at large distances. Although QCD is not conformally invariant, one can nevertheless use the mathematical representation of the conformal group in five-dimensional anti-de Sitter space to construct a first approximation to the theory. The AdS/CFT correspondence also provides insights into the inherently non-perturbative aspects of QCD, such as the orbital and radial spectra of hadrons and the form of hadronic wavefunctions. In particular, we show that there is an exact correspondence between the fifth-dimensional coordinate of AdS space z and a specific impact variable {zeta} which measures the separation of the quark and gluonic constituents within the hadron in ordinary space-time. This connection allows one to compute the analytic form of the frame-independent light-front wavefunctions, the fundamental entities which encode hadron properties and allow the computation of decay constants, form factors, and other exclusive scattering amplitudes. New relativistic lightfront equations in ordinary space-time are found which reproduce the results obtained using the 5-dimensional theory. The effective light-front equations possess remarkable algebraic structuresmore » and integrability properties. Since they are complete and orthonormal, the AdS/CFT model wavefunctions can also be used as a basis for the diagonalization of the full light-front QCD Hamiltonian, thus systematically improving the AdS/CFT approximation.« less

Authors:
; ; ;
Publication Date:
Research Org.:
Stanford Linear Accelerator Center (SLAC)
Sponsoring Org.:
USDOE
OSTI Identifier:
899840
Report Number(s):
SLAC-PUB-12361
TRN: US0702104
DOE Contract Number:
AC02-76SF00515
Resource Type:
Conference
Resource Relation:
Conference: Invited talk at 2006 International Workshop on the Origin of Mass and Strong Coupling Gauge Theories (SCGT 06), Nagoya, Japan, 21-24 Nov 2006
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; APPROXIMATIONS; COLOR; CONFINEMENT; CONFORMAL GROUPS; DECAY; FORM FACTORS; HADRONS; ORIGIN; QUANTUM CHROMODYNAMICS; QUARKS; SCALE INVARIANCE; SCATTERING AMPLITUDES; SPACE-TIME; SPECTRA; Theory-HEP,HEPPH, HEPTH

Citation Formats

Brodsky, Stanley J., /SLAC, de Teramond, Guy F., and /Costa Rica U. /SLAC. ADS/CFT and QCD. United States: N. p., 2007. Web.
Brodsky, Stanley J., /SLAC, de Teramond, Guy F., & /Costa Rica U. /SLAC. ADS/CFT and QCD. United States.
Brodsky, Stanley J., /SLAC, de Teramond, Guy F., and /Costa Rica U. /SLAC. Wed . "ADS/CFT and QCD". United States. doi:. https://www.osti.gov/servlets/purl/899840.
@article{osti_899840,
title = {ADS/CFT and QCD},
author = {Brodsky, Stanley J. and /SLAC and de Teramond, Guy F. and /Costa Rica U. /SLAC},
abstractNote = {The AdS/CFT correspondence between string theory in AdS space and conformal .eld theories in physical spacetime leads to an analytic, semi-classical model for strongly-coupled QCD which has scale invariance and dimensional counting at short distances and color confinement at large distances. Although QCD is not conformally invariant, one can nevertheless use the mathematical representation of the conformal group in five-dimensional anti-de Sitter space to construct a first approximation to the theory. The AdS/CFT correspondence also provides insights into the inherently non-perturbative aspects of QCD, such as the orbital and radial spectra of hadrons and the form of hadronic wavefunctions. In particular, we show that there is an exact correspondence between the fifth-dimensional coordinate of AdS space z and a specific impact variable {zeta} which measures the separation of the quark and gluonic constituents within the hadron in ordinary space-time. This connection allows one to compute the analytic form of the frame-independent light-front wavefunctions, the fundamental entities which encode hadron properties and allow the computation of decay constants, form factors, and other exclusive scattering amplitudes. New relativistic lightfront equations in ordinary space-time are found which reproduce the results obtained using the 5-dimensional theory. The effective light-front equations possess remarkable algebraic structures and integrability properties. Since they are complete and orthonormal, the AdS/CFT model wavefunctions can also be used as a basis for the diagonalization of the full light-front QCD Hamiltonian, thus systematically improving the AdS/CFT approximation.},
doi = {},
journal = {},
number = ,
volume = ,
place = {United States},
year = {Wed Feb 21 00:00:00 EST 2007},
month = {Wed Feb 21 00:00:00 EST 2007}
}

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  • The light-front quantization of gauge theories in light-cone gauge provides a frame-independent wavefunction representation of relativistic bound states, simple forms for current matrix elements, explicit unitarity, and a Fock space built on a trivial vacuum. The AdS/CFT correspondence has led to important insights into the properties of quantum chromodynamics even though QCD is a broken conformal theory. We have recently shown how a model based on a truncated AdS space can be used to obtain the hadronic spectrum of q{bar q}, qqq and gg bound states, as well as their respective light-front wavefunctions. Specific hadrons are identified by the correspondencemore » of string modes with the dimension of the interpolating operator of the hadron's valence Fock state, including orbital angular momentum excitations. The predicted mass spectrum is linear M {proportional_to} L at high orbital angular momentum, in contrast to the quadratic dependence M{sup 2}/L found in the description of spinning strings. Since only one parameter, the QCD scale {Lambda}{sub QCD}, is introduced, the agreement with the pattern of physical states is remarkable. In particular, the ratio of {Delta} to nucleon trajectories is determined by the ratio of zeros of Bessel functions. As a specific application of QCD dynamics from AdS/CFT duality, we describe a computation of the proton magnetic form factor in both the space-like and time-like regions. The extended AdS/CFT space-time theory also provides an analytic model for hadronic light-front wavefunctions, thus providing a relativistic description of hadrons in QCD at the amplitude level. The model wavefunctions display confinement at large inter-quark separation and conformal symmetry at short distances. In particular, the scaling and conformal properties of the LFWFs at high relative momenta agree with perturbative QCD. These AdS/CFT model wavefunctions could be used as an initial ansatz for a variational treatment of the light-front QCD Hamiltonian.« less
  • The AdS/CFT correspondence has led to important insights into the properties of quantum chromodynamics even though QCD is a broken conformal theory. We have recently shown how a holographic model based on a truncated AdS space can be used to obtain the hadronic spectrum of light q{bar q}, qqq and gg bound states. Specific hadrons are identified by the correspondence of string modes with the dimension of the interpolating operator of the hadron's valence Fock state, including orbital angular momentum excitations. The predicted mass spectrum is linear M {proportional_to} L at high orbital angular momentum, in contrast to the quadraticmore » dependence M{sup 2} {proportional_to} L found in the description of spinning strings. Since only one parameter, the QCD scale LQCD, is introduced, the agreement with the pattern of physical states is remarkable. In particular, the ratio of D to nucleon trajectories is determined by the ratio of zeros of Bessel functions. The light-front quantization of gauge theories in light-cone gauge provides a frame-independent wavefunction representation of relativistic bound states, simple forms for current matrix elements, explicit unitarity, and a trivial vacuum. The light-front Fock-state wavefunctions encode the bound state properties of hadrons in terms of their quark and gluon degrees of freedom at the amplitude level. One can also use the extended AdS/CFT space-time theory to obtain a model for hadronic light-front wavefunctions, thus providing a relativistic description of hadrons in QCD at the amplitude level. The model wavefunctions display confinement at large inter-quark separation and conformal symmetry at short distances. In particular, the scaling and conformal properties of the LFWFs at high relative momenta agree with perturbative QCD. These AdS/CFT model wavefunctions could be used as an initial ansatz for a variational treatment of the light-front QCD Hamiltonian. We also show how hadron form factors in both the space-like and time-like regions can be predicted.« less
  • Even though quantum chromodynamics is a broken conformal theory, the AdS/CFT correspondence has led to important insights into the properties of QCD. For example, as shown by Polchinski and Strassler, dimensional counting rules for the power-law falloff of hadron scattering amplitudes follow from dual holographic models with conformal behavior at short distances and confinement at large distances. We find that one also obtains a remarkable representation of the entire light-quark meson and baryon spectrum, including all orbital excitations, based on only one mass parameter. We also show how hadron light-front wavefunctions and hadron form factors in both the space-like andmore » time-like regions can be predicted.« less
  • The AdS/CFT correspondence is a powerful tool to study the properties of conformal QCD at strong coupling in terms of a higher dimensional dual gravity theory. The power-law falloff of scattering amplitudes in the non-perturbative regime and calculable hadron spectra follow from holographic models dual to QCD with conformal behavior at short distances and confinement at large distances. String modes and fluctuations about the AdS background are identified with QCD degrees of freedom and orbital excitations at the AdS boundary limit. A description of form factors in space and time-like regions and the behavior of light-front wave functions can alsomore » be understood in terms of a dual gravity description in the interior of AdS.« less
  • The AdS/CFT correspondence between conformal field theory and string states in an extended space-time has provided new insights into not only hadron spectra, but also their light-front wavefunctions. We show that there is an exact correspondence between the fifth-dimensional coordinate of anti-de Sitter space z and a specific impact variable {zeta} which measures the separation of the constituents within the hadron in ordinary space-time. This connection allows one to predict the form of the light-front wavefunctions of mesons and baryons, the fundamental entities which encode hadron properties and scattering amplitudes. A new relativistic Schroedinger light-cone equation is found which reproducesmore » the results obtained using the fifth-dimensional theory.« less