QCD and Light-Front Holography

Few Body Systems, 2014

Physical Review D, 2008

Chinese Physics C, 2010

The combination of Anti-de Sitter space (AdS) methods with light-front holography leads to a semi-classical first approximation to the spectrum and wavefunctions of meson and baryon light-quark bound states. Starting from the bound-state Hamiltonian equation of motion in QCD, we derive relativistic lightfront 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. Its eigenvalues give the hadronic spectrum, and its eigenmodes represent the probability distributions of the hadronic constituents at a given scale. Applications to the light meson and baryon spectra are presented. The predicted meson spectrum has a string-theory Regge form M 2 = 4κ 2 (n+L+S/2); i.e., the square of the eigenmass is linear in both L and n, where n counts the number of nodes of the wavefunction in the radial variable ζ. The space-like pion and nucleon form factors are also well reproduced. One thus obtains a remarkable connection between the description of hadronic modes in AdS space and the Hamiltonian formulation of QCD in physical space-time quantized on the light-front at fixed light-front time τ. The model can be systematically improved by using its complete orthonormal solutions to diagonalize the full QCD lightfront Hamiltonian or by applying the Lippmann-Schwinger method in order to systematically include the QCD interaction terms.

Light-Front Hamiltonian theory, derived from the quantization of the QCD Lagrangian at fixed lightfront time τ = x 0 + x 3 , provides a rigorous frame-independent framework for solving nonperturbative QCD. The eigenvalues of the light-front QCD Hamiltonian HLF predict the hadronic mass spectrum, and the corresponding eigensolutions provide the light-front wavefunctions which describe hadron structure. In the case of mesons, the valence Fock-state wavefunctions of HLF for zero quark mass satisfy a singlevariable relativistic equation of motion in the invariant variable ζ 2 = b 2 ⊥ x(1 − x), which is conjugate to the invariant mass squared M 2 qq. The effective confining potential U (ζ 2) in this frame-independent "light-front Schrödinger equation" systematically incorporates the effects of higher quark and gluon Fock states. Remarkably, the potential has a unique form of a harmonic oscillator potential if one requires that the chiral QCD action remains conformally invariant. The result is a nonperturbative relativistic light-front quantum mechanical wave equation which incorporates color confinement and other essential spectroscopic and dynamical features of hadron physics. Anti-de Sitter space in five dimensions plays a special role in elementary particle physics since it provides an exact geometrical representation of the conformal group. Remarkably, gravity in AdS5 space is holographically dual to frame-independent light-front Hamiltonian theory. 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 ζ, the argument of the boost-invariant light-front wavefunctions describing the internal structure of hadrons in physical space-time. The holographic mapping of gravity in AdS space to QCD with a specific "soft-wall" dilaton yields the confining potential U (ζ 2) which is consistent with conformal invariance of the QCD action and the light-front Schrödinger equation, extended to hadrons with arbitrary spin J. 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 mq → 0 limit, and linear Regge trajectories M 2 (n, L) ∝ 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 thus gives a frame-independent representation of color-confining dynamics, Regge spectroscopy, as well as the excitation spectra of relativistic light-quark meson and also 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.

2010

AdS/QCD, the correspondence between theories in a dilaton-modified five-dimensional anti-de Sitter space and confining field theories in physical space-time, provides a remarkable semiclassical model for hadron physics. Light-front holography allows hadronic amplitudes in the AdS fifth dimension to be mapped to frame-independent light-front wavefunctions of hadrons in physical space-time. The result is a single-variable light-front Schrodinger equation which determines the eigenspectrum and the light-front wavefunctions of hadrons for general spin and orbital angular momentum. The coordinate z in AdS space is uniquely identified with a Lorentz-invariant coordinate zeta which measures the separation of the constituents within a hadron at equal light-front time and determines the off-shell dynamics of the bound state wavefunctions as a function of the invariant mass of the constituents. The hadron eigenstates generally have components with different orbital angular momentum; e.g., the...

We describe a procedure to extend the light-front holographic approach to hadronic physics to include light-quark masses. The proposed framework allows us to extend the formalism of de Alfaro, Fubini and Furlan to the frame-independent light-front Hamiltonian theory in the approximation where the dynamics in the invariant transverse variable is unchanged to first order in the quark masses. The confinement potential follows from an effective theory which encodes the fundamental conformality of the classical QCD Lagrangian and leads to a semiclassical relativistic light-front wave equation for arbitrary spin. In particular, the K meson spectrum is successfully described without modifying the emerging confinement scale. The Wilson loop criteria for confinement is maintained, since for light quark masses a harmonic potential and linear Regge trajectories in the light-front form of dynamics corresponds to a linear potential in the usual instant-form.

Journal of Physics: Conference Series, 2011

We give an overview of the light-front holographic approach to strongly coupled QCD, whereby a confining gauge theory, quantized on the light front, is mapped to a higher-dimensional anti de Sitter (AdS) space. The framework is guided by the AdS/CFT correspondence incorporating a gravitational background asymptotic to AdS space which encodes the salient properties of QCD, such as the ultraviolet conformal limit at the AdS boundary at z → 0, as well as modifications of the geometry in the large z infrared region to describe confinement and linear Regge behavior. There are two equivalent procedures for deriving the AdS/QCD equations of motion: one can start from the Hamiltonian equation of motion in physical space time by studying the off-shell dynamics of the bound state wavefunctions as a function of the invariant mass of the constituents. To a first semiclassical approximation, where quantum loops and quark masses are not included, this leads to a lightfront Hamiltonian equation which describes the bound state dynamics of light hadrons in terms of an invariant impact variable ζ which measures the separation of the partons within the hadron at equal light-front time. Alternatively, one can start from the gravity side by studying the propagation of hadronic modes in a fixed effective gravitational background. Both approaches are equivalent in the semiclassical approximation. This allows us to identify the holographic variable z in AdS space with the impact variable ζ. Light-front holography thus allows a precise mapping of transition amplitudes from AdS to physical space-time. The internal structure of hadrons is explicitly introduced and the angular momentum of the constituents plays a key role.

2016

Light-Front Hamiltonian theory, derived from the quantization of the QCD La-grangian at fixed light-front time τ = t + z/c, provides a rigorous frame-independent framework for solving nonperturbative QCD. The eigenvalues of the light-front QCD Hamiltonian predict the hadronic mass spectrum, and the corresponding eigensolutions provide the light-front wavefunctions which describe hadron structure. The valence Fock-state wavefunctions of the light-front QCD Hamiltonian satisfy a single-variable relativistic equation of motion, analogous to the nonrelativistic radial Schrödinger equa-tion, with an effective confining potential U which systematically incorporates the ef-fects of higher quark and gluon Fock states. In fact, the potential U has a unique form if one requires that the action for zero quark mass remains conformally invariant. We also show that the holographic mapping of gravity in AdS space to QCD with a specific soft-wall dilaton yields the same light-front Schrödinger eq...

Communications in Theoretical Physics, 2012

Light-Front Holography leads to a rigorous connection between hadronic amplitudes in a higher dimensional anti-de Sitter (AdS) space and frame-independent light-front wavefunctions of hadrons in 3 + 1 physical space-time, thus providing a compelling physical interpretation of the AdS/CFT correspondence principle and AdS/QCD, a useful framework which describes the correspondence between theories in a modified AdS 5 background and confining field theories in physical space-time. To a first semiclassical approximation, where quantum loops and quark masses are not included, this approach leads to a single-variable light-front Schrödinger equation which determines the eigenspectrum and the light-front wavefunctions of hadrons for general spin and orbital angular momentum. The coordinate z in AdS space is uniquely identified with a Lorentz-invariant coordinate ζ which measures the separation of the constituents within a hadron at equal light-front time. The internal structure of hadrons is explicitly introduced and the angular momentum of the constituents plays a key role. We give an overview of the light-front holographic approach to strongly coupled QCD. In particular, we study the photon-to-meson transition form factors (TFFs) F M γ (Q 2) for γγ * → M using light-front holographic methods. The results for the TFFs for the η and η mesons are also presented. Some novel features of QCD are discussed, including the consequences of confinement for quark and gluon condensates. A method for computing the hadronization of quark and gluon jets at the amplitude level is outlined.

Few-Body Systems, 2013