Applications of AdS/CFT Duality to QCD

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 and time-like regions can be predicted.Comment: Invited Talk, presented at the International Conference on QCD and Hadronic Physics, Jun 16-20, 200

Light-Front Holographic Quantum Chromodynamics

Anti-de Sitter space in five dimensions provides an exact geometrical representation of the conformal group. Remarkably, gravity in AdS$_5$ space is holographically dual to frame-independent light-front Hamiltonian theory, derived from the quantization of the QCD Lagrangian at fixed light-front time $\tau = x^0+x^3$. Light-front holography also leads to a precise relation between the bound-state amplitudes in the fifth dimension $z$ of AdS space and the variable $\zeta$, where $\zeta^2 = b^2_\perp x(1-x)$ is the argument of the boost-invariant light-front wavefunctions describing the internal structure of hadrons in physical space-time. The holographic mapping of AdS space with a specific "soft-wall" dilaton yields a confining potential $U(\zeta^2)$ for the light-front Schr\"odinger equation for hadrons with arbitrary spin $J$. Remarkably, $U(\zeta^2)$ has a unique form of a harmonic oscillator potential if one requires that the chiral QCD action remains conformally invariant. One thus obtains an effective light-front effective theory for general spin which respects the conformal symmetry of the four-dimensional classical QCD Lagrangian. The predictions of the LF equations of motion include a zero-mass pion in the chiral $m_q\to 0$ limit, and linear Regge trajectories $M^2(n,L) \propto n+L$ with the same slope in the radial quantum number $n$ and the orbital angular momentum $L$. The light-front AdS/QCD holographic approach gives a frame-independent representation of color-confining dynamics, Regge spectroscopy, as well as the excitation spectra of relativistic light-quark meson and baryon bound states in QCD in terms of a single mass parameter. We also briefly discuss the implications of the underlying conformal template of QCD for renormalization scale-setting, and the implications of light-front quantization for the value of the cosmological constant.Comment: Presented by SJB at the International Conference on Nuclear Theory in the Supercomputing Era (NTSE 2013) in honor of James Vary, May 13 - May 17, 2013, Iowa State University, Ames, Iow

Light-Front Holography: A First Approximation to QCD

Starting from the Hamiltonian equation of motion in QCD, we identify an invariant light-front coordinate $\zeta$ which allows the separation of the dynamics of quark and gluon binding from the kinematics of constituent spin and internal orbital angular momentum. The result is a single variable light-front Schrodinger equation for QCD which determines the eigenspectrum and the light-front wavefunctions of hadrons for general spin and orbital angular momentum. This light-front wave equation is equivalent to the equations of motion which describe the propagation of spin-$J$ modes on anti-de Sitter (AdS) space.Comment: 4 pages. The limits of validity of the model are further discussed. To appear in Physical Review Letter

Hadronic Spectrum of a Holographic Dual of QCD

We compute the spectrum of light hadrons in a holographic dual of QCD defined on $AdS_5 \times S^5$ which has conformal behavior at short distances and confinement at large interquark separation. Specific hadrons are identified by the correspondence of string modes with the dimension of the interpolating operator of the hadron's valence Fock state. Higher orbital excitations are matched quanta to quanta with fluctuations about the AdS background. Since only one parameter, the QCD scale $\Lambda_{QCD}$, is used, 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.Comment: 4 pages, REVTeX4, 2 figures. Version published in Phys. Rev. Let