Light-Front Holography, a remarkable feature of the AdS/CFT correspondence, maps amplitudes in anti-de Sitter (AdS) space to frame-independent light-front wavefunctions of hadrons in physical space-time. The model leads to an effective confining light-front QCD Hamiltonian and 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 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 and the fall-off in the invariant mass of the constituents. The soft-wall holographic model, modified by a positive-sign dilaton metric, leads to a remarkable one-parameter description of nonperturbative hadron dynamics -- a semi-classical frame-independent first approximation to the spectra and light-front wavefunctions of meson and baryons. The model predicts a Regge spectrum of linear trajectories with the same slope in the leading orbital angular momentum L of hadrons and the radial quantum number n. The hadron eigensolutions projected on the free Fock basis provides the complete set of valence and non-valence light-front Fock state wavefunctions which describe the hadron's momentum and spin distributions needed to compute measures of hadron structure at the quark and gluon level. The effective confining potential also creates quark- antiquark pairs. The AdS/QCD model can be systematically improved by using its complete orthonormal solutions to diagonalize the full QCD light-front Hamiltonian or by applying the Lippmann-Schwinger method to systematically include the QCD interaction terms. A new perspective on quark and gluon condensates is also presented.
Using ideas from Light Front Holography, we discuss the calculation of hadronic properties. In this talk I will pay special attention to hadronic masses and the nucleon helicity-independent generalized parton distributions of quarks in the zero skewness case
We reply to L. Ya. Glozman's Comment "Is a consistent holographic description of excited hadrons with fixed $L$ possible?" In general, the solutions of the bound state Hamiltonian equation of motion in QCD have Fock state components with different $L$, and consequently hadronic relativistic wave equations derived in the framework of light-front holography share this property. For example, the proton eigenstate has components with L=0 and L=1. The results of AdS/QCD are consistent with the requirements of chiral symmetry and do not violate any fundamental physical principle. This is further ill…
Starting from the Hamiltonian equation of motion in QCD, we identify an invariant light-front coordinate $ζ$ 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 (A…
Light-Front Holography is a remarkable consequence of the correspondence between string theory in AdS space and conformal field theories in physical-space time. It allows string modes $Φ(z)$ in the AdS fifth dimension to be precisely mapped to the light-front wavefunctions of hadrons in terms of a specific light-front impact variable $ζ$ which measures the separation of the quark and gluonic constituents within the hadron. This mapping was originally obtained by matching the exact expression for electromagnetic current matrix elements in AdS space with the corresponding exact expression for th…
I survey recent developments in hadron physics which follow from the application of superconformal quantum mechanics and light-front holography. This includes new insights into the physics of color confinement, chiral symmetry, the spectroscopy and dynamics of hadrons, as well as surprising supersymmetric relations between the masses of mesons, baryons, and tetraquarks. I also will discuss some novel features of QCD -- such as color transparency, hidden color, and asymmetric intrinsic heavy-quark phenomena. The elimination of renormalization scale ambiguities and the modification of QCD sum ru…
One of the most important nonperturbative methods for solving QCD is quantization at fixed light-front time, τ= t+z/c -- Dirac's "Front Form". The eigenvalues of the light-front QCD Hamiltonian predict the hadron spectrum and the eigensolutions provide the light-front wavefunctions which describe hadron structure. More generally, we show that 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 equation, with an effective confining potential U which systematically i…
Light-front holography allows hadronic amplitudes in the AdS/QCD fifth dimension to be mapped to frame-independent light-front wavefunctions of hadrons in physical space-time, thus providing a relativistic description of hadrons at the amplitude level. The AdS coordinate z is identified with an invariant light-front coordinate zeta which separates 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 wav…
The eigenvalues of the light-front QCD Hamiltonian, quantized at fixed light-front time τ= t+z/c, predict the hadronic mass spectrum and the corresponding eigensolutions provide the light-front wavefunctions which describe hadron structure. More generally, we show that 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 equation, with an effective confining potential $U$ which systematically incorporates the effects of higher quark and gluon Fock states. We outline…
We summarize the light-front coupled-cluster (LFCC) method for the solution of field-theoretic bound-state eigenvalue problems and indicate the connection with light-front holographic QCD. This includes a sample application of the LFCC method and leads to a relativistic quark model for mesons that adds longitudinal dynamics to the usual transverse light-front holographic Schrodinger equation.
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 a…
Light-front holography offers a successful first semiclassical approximation to hadronic spectroscopy and dynamics. We review its underlying assumptions, its remarkable predictions as well as attempts to go beyond the semiclassical approximation in order to the describe a wide range of data with a universal AdS/QCD mass scale.
Gauge/gravity duality leads to a simple, analytical, and phenomenologically compelling nonperturbative approximation to the full light-front QCD Hamiltonian. This approach, called "Light-Front Holography", successfully describes the spectroscopy of light-quark meson and baryons, their elastic and transition form factors, and other hadronic properties. The bound-state Schrodinger and Dirac equations of the soft-wall AdS/QCD model predict linear Regge trajectories which have the same slope in orbital angular momentum L and radial quantum number n for both mesons and baryons. Light-front holograp…
The correspondence between theories in anti-de Sitter space and conformal field theories in physical space-time leads to an analytic, semiclassical model for strongly-coupled QCD. 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, thus providing a relativistic description of hadrons at the amplitude level. We identify the AdS coordinate $z$ with an invariant light-front coordinate $ζ$ which separates the dynamics of quark and gluon binding from the kinematics of constituent …
We give an overview of recent progress into the infrared structure of QCD based on the gauge/gravity correspondence and light-front quantization, where the color confining interaction for mesons and baryons is determined by an underlying superconformal algebraic structure. This new approach to hadron physics gives remarkable connections and predictions across the entire mass spectrum of hadrons and also describes the infrared behavior of the strong coupling. More recently, an extensive study of form factors, polarized and unpolarized parton distributions and the sea quark contribution to the n…
The holographic mapping of gravity in AdS space to QCD, quantized at fixed light-front time, provides a precise relation between the bound-state amplitudes in the fifth dimension of AdS space and the boost-invariant light-front wavefunctions describing the internal structure of hadrons in physical space-time. In particular, the elastic and transition form factors of the pion and the nucleons are well described in this framework. The light-front AdS/QCD holographic approach thus gives a frame-independent first approximation of the color-confining dynamics, spectroscopy, and excitation spectra o…
Light-Front Quantization -- Dirac's "Front Form" -- provides a physical, frame-independent formalism for hadron dynamics and structure. Observables such as structure functions, transverse momentum distributions, and distribution amplitudes are defined from the hadronic LFWFs. One obtains new insights into the hadronic mass scale, the hadronic spectrum, and the functional form of the QCD running coupling in the nonperturbative domain using light-front holography. In addition, superconformal algebra leads to remarkable supersymmetric relations between mesons and baryons. I also discuss evidence …
Starting from the bound state Hamiltonian equation of motion in QCD, we derive 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. Its eigenvalues give the hadronic spectrum, and its eigenmodes represent the probability amplitudes of the hadronic constituents at a given scale. An e…
I review applications of superconformal algebra. light-front holography, and an extended form of conformal symmetry to hadron spectroscopy and dynamics. QCD is not supersymmetrical in the traditional sense -- the QCD Lagrangian is based on quark and gluonic fields -- not squarks nor gluinos. However, its hadronic eigensolutions conform to a representation of superconformal algebra. and provide a unified Regge spectroscopy of meson, baryon, and tetraquarks with a universal Regge slope. The pion $q \bar q$ eigenstate is composite but yet has zero mass for $m_q=0.$ Light-Front Holography also pre…
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 p…
The correspondence between theories in anti-de Sitter space and field theories in physical space-time leads to an analytic, semiclassical model for strongly-coupled QCD which has scale invariance at short distances and color confinement at large distances. These equations, for both mesons and baryons, give a very good representation of the observed hadronic spectrum, including a zero mass pion. 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, thus providing a relativistic …
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 …
The soft-wall AdS/QCD model, modified by a positive-sign dilaton metric, leads to a remarkable one-parameter description of nonperturbative hadron dynamics. The model predicts a zero-mass pion for zero-mass quarks and a Regge spectrum of linear trajectories with the same slope in the leading orbital angular momentum $L$ of hadrons and the radial quantum number $N$. Light-Front Holography maps the amplitudes which are functions of the fifth dimension variable $z$ of anti-de Sitter space to a corresponding hadron theory quantized on the light front. The resulting Lorentz-invariant relativistic l…
We evaluate the cross section for the pion induced Drell-Yan process in two different models of the pion light-front wave function, inspired by light-front holographic approaches. We obtain the valence quark distribution functions in those models, which after QCD evolution, are consistent with the experimental data from the E-0615 experiment at Fermilab. Supplemented by the parton distribution functions of the target nuclei, we obtain the cross section consistent with the experimental data for the $π^-$ Nucleus $\rightarrow {μ^+μ^-X}$ Drell-Yan process.
A remarkable holographic feature of dynamics in AdS space in five dimensions is that it is dual to Hamiltonian theory in physical space-time, quantized at fixed light-front time τ = t+z/c. This light-front holographic principle provides a precise relation between the bound-state amplitudes in AdS space and the boost-invariant light-front wavefunctions describing the internal structure of hadrons in physical space-time. The fifth dimension coordinate z is dual to the light front variable ζ describing the invariant separation of the quark constituents. The resulting valence Fock-state wavefuncti…
We show how the string amplitude $Φ(z)$ defined on the fifth dimension in AdS$_5$ space can be precisely mapped to the light-front wavefunctions of hadrons in physical spacetime. We find an exact correspondence between the holographic variable $z$ and an impact variable $ζ$, which represents the measure of transverse separation of the constituents within the hadrons. In addition, we derive effective four dimensional Schrödinger equations for the bound states of massless quarks and gluons which exactly reproduce the AdS/CFT results and give a realistic description of the light-quark meson and b…
We present an analytically solvable 3D light-front Hamiltonian model for hadrons that extends light-front holography by including finite mass quarks and a longitudinal confinement term. We propose that the model is suitable as an improved analytic approximation to QCD at a low resolution scale. We demonstrate that it preserves desired Lorentz symmetries and it produces improved agreement with the experimental mass spectroscopy and other properties of the light mesons. Importantly, the model also respects chiral symmetry and the Gell-Mann-Oakes-Renner relation.
To a first semiclassical approximation one can reduce the multi-parton light-front problem in QCD to an effective one-dimensional quantum field theory, which encodes the fundamental conformal symmetry of the classical QCD Lagrangian. This procedure leads to a relativistic light-front wave equation for arbitrary spin which incorporates essential spectroscopic and non-perturbative dynamical features of hadron physics. The mass scale for confinement and higher dimensional holographic mapping to AdS space are also emergent properties of this framework.
Superconformal algebra leads to remarkable connections between the masses of mesons and baryons of the same parity -- supersymmetric relations between the bosonic and fermionic bound states of QCD. Supercharges connect the mesonic eigenstates to their baryonic superpartners, where the mesons have internal angular momentum one unit higher than the baryons. We also predict the existence of tetraquarks which are degenerate in mass with baryons with the same angular momentum. An effective supersymmetric light-front Hamiltonian for hadrons composed of light quarks can be constructed by embedding su…
Using light-front holography, we predict simultaneously the pion decay constant and the pion charge radius by taking into account (higher twist) dynamical spin effects whose relative importance is constrained by QCD.
The QCD light-front Hamitonian equation derived from quantization at fixed LF time provides a causal, frame-independent, method for computing hadron spectroscopy and dynamical observables. de Alfaro, Fubini, and Furlan (dAFF) have made an important observation that a mass scale can appear in the equations of motion without affecting the conformal invariance of the action if one adds a term to the Hamiltonian proportional to the dilatation operator or the special conformal operator. If one applies the dAFF procedure to the QCD light-front Hamiltonian, it leads to a color confining potential $κ^…
We use AdS/QCD holographic Distributions Amplitudes for the vector mesons $ρ$ and $K^*$ in order to predict the radiative decays $B \to ργ$ and $B \to K^* γ$ as well as the semileptonic decays $B \to ρl ν$ and $B \to K^* μ^+ μ^-$. For the radiative decays, we find that the AdS/QCD DAs offer the advantage of avoiding end-point singularities when computing power suppressed contributions. For the semileptonic decays $B \to ρl ν$ and $B \to K^* μ^+ μ^-$, we compare our predictions to the latest BaBar and LHCb data respectively.
The anomalous dimensions of hadronic interpolators contain dynamical information on the properties of the associated hadron states. We point out that they provide, in particular, a link by which gauge-invariant information on exotic contributions to hadronic wavefunctionals can be obtained from approximate gravity duals for QCD. This is demonstrated by the holographic description of a dominant tetraquark component in the lightest scalar mesons.
AdS/QCD, the correspondence between theories in a 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, thus providing a relativistic description of hadrons at the amplitude level. We identify the AdS coordinate $z$ with an invariant light-front coordinate $ζ$ which separates the dynamics of quark and gluon binding fro…
The light-front holographic mapping of classical gravity in AdS space, modified by a positive-sign dilaton background, leads to a nonperturbative effective coupling $α_s^{AdS}(Q^2)$. It agrees with hadron physics data extracted from different observables, such as the effective charge defined by the Bjorken sum rule, as well as with the predictions of models with built-in confinement and lattice simulations. It also displays a transition from perturbative to nonperturbative conformal regimes at a momentum scale $ \sim 1$ GeV. The resulting $β$ function appears to capture the essential character…
QCD is well understood at short distances where perturbative calculations are feasible. Establishing an explicit analytic connection between the short-distance regime and the large-distance physics of quark confinement has been a long-sought goal. A major challenge is to relate the scale $Λ_{s}$ underlying the evolution of the QCD coupling in the perturbative regime to the masses of hadrons. We show here how new theoretical insights into the behavior of QCD at large distances leads to such a relation. The resulting prediction for $Λ_{s}$ in the $\overline{MS}$ scheme agrees well with experimen…
We compute the rate for diffractive $ϕ$ electro-production using the Color Glass Condensate dipole model. The model parameters are obtained from fits to the most recent combined HERA data on inclusive deep inelastic scattering. As for the $ϕ$ meson, we use an AdS/QCD holographic light front wavefunction. Our predictions are compared to the available data collected at the HERA collider.
We account for dynamical spin effects in the holographic light-front wavefunction of the pion in order to predict its mean charge radius, decay constant, spacelike electromagnetic form factor, twist-2 Distribution Amplitude and the photon-to-pion transition form factor. Using a universal fundamental AdS/QCD scale of 523 MeV and a constituent quark mass of 330 MeV, we find a remarkable improvement in describing all observables.
We investigate the tree level multi-gluon components of the gluon light cone wavefunctions in the light cone gauge keeping the exact kinematics of the gluon emissions. We focus on the components with all helicities identical to the helicity of the incoming gluon. The recurrence relations for the gluon wavefunctions are derived. In the case when the virtuality of the incoming gluon is neglected the exact form of the multi-gluon wavefunction as well as the fragmentation function is obtained. Furthermore we analyze the 2 to N tree-level gluon scattering in the framework of light-front perturbatio…
We use an anti-de Sitter/Quantum Chromodynamics (AdS/QCD) holographic light-front wavefunction for the $ρ$ and $ϕ$ mesons, in conjunction with the Color Glass Condensate (CGC) dipole cross-section whose parameters are fitted to the most recent 2015 high precision HERA data on inclusive Deep Inelastic Scattering (DIS), in order to predict the cross-sections for diffractive $ρ$ and $ϕ$ electroproduction. Our results suggest that the holographic meson light-front wavefunction is able to give a simultaneous description of the $ρ$ and $ϕ$ production data provided we use a set of light quark masses …
QCD is not supersymmetrical in the traditional sense -- the QCD Lagrangian is based on quark and gluonic fields, not squarks nor gluinos. However, its hadronic eigensolutions conform to a representation of superconformal algebra, reflecting the underlying conformal symmetry of chiral QCD and its Pauli matrix representation. The eigensolutions of superconformal algebra provide a unified Regge spectroscopy of meson, baryon, and tetraquarks in the same 4-plet representation with a universal Regge slope. The pion $q \bar q$ eigenstate has zero mass for $m_q=0.$ The superconformal relations also ca…
The correspondence between theories in anti-de Sitter space and conformal field theories in physical space-time leads to an analytic, semiclassical model for strongly-coupled QCD which has scale invariance at short distances and color confinement at large distances. Light-front holography is a remarkable feature of AdS/CFT: it allows hadronic amplitudes in the AdS fifth dimension to be mapped to frame-independent light-front wavefunctions of hadrons in physical space-time, thus providing a relativistic description of hadrons at the amplitude level. Some novel features of QCD are discussed, inc…
A general procedure for obtaining frame-independent, three-dimensional light-front coordinate-space wave functions is introduced. The third spatial coordinate, $\tilde z$ , is the frame independent coordinate conjugate to the light-front momentum coordinate $x={k^+\over P^+}$ which appears in the momentum-space light-front wave functions underlying generalized parton distributions, structure functions, distribution amplitudes, form factors, and other hadronic observables. These causal light-front coordinate-space wave functions are used to derive a general expression for the quark distribution…
A fundamental goal in QCD is to understand the non-perturbative structure of hadrons at the amplitude level--not just the single-particle flavor, momentum, and helicity distributions of the quark constituents, but also the multi-quark, gluonic, and hidden-color correlations intrinsic to hadronic and nuclear wavefunctions. A natural calculus for describing the bound-state structure of relativistic composite systems in quantum field theory is the light-front Fock expansion which encodes the properties of a hadrons in terms of a set of frame-independent n-particle wavefunctions. Light-front quant…
Following a recent suggestion by Randall and Sundrum, we consider string compactification scenarios in which a compact slice of AdS-space arises as a subspace of the compactification manifold. A specific example is provided by the type II orientifold equivalent to type I theory on (orbifolds of) $T^6$, upon taking into account the gravitational backreaction of the D3-branes localized inside the $T^6$. The conformal factor of the four-dimensional metric depends exponentially on one of the compact directions, which, via the holographic correspondence, becomes identified with the renormalization …
We present analytic parametrizations for the $γ^\ast N \to N(1440)$ form factors derived from light-front holography in leading twist approximation. The new parametrizations describe the electromagnetic form factors using analytic functions dependent on the masses of the $ρ$ meson and respective radial excitations, as well as the masses of the nucleon and the resonance $N(1440)$. The free parameters of the model, associated with three independent couplings, are interpreted as bare couplings, and are fixed by the nucleon data for large $Q^2$. The proposed parametrizations compare remarkably wel…
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 light-front wave equations in terms of an invariant impact variable zeta 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 prop…
Light-Front Quantization provides a physical, frame-independent formalism for hadron dynamics and structure. Observables such as structure functions, transverse momentum distributions, and distribution amplitudes are defined from the hadronic light-front wavefunctions. One obtains new insights into the hadronic spectrum, light-front wavefunctions, and the functional form of the QCD running coupling in the nonperturbative domain using light-front holography -- the duality between the front form and AdS$_5$, the space of isometries of the conformal group. In addition, superconformal algebra lead…
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 light-front wave equations in terms of an invariant impact variable zeta 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 prop…
We construct spin-improved holographic light front wavefunctions for the nucleons (viewed as quark-diquark systems) and use them to successfully predict their electromagnetic Sachs form factors, their electromagnetic charge radii, as well as the axial form factor, charge and radius of the proton. The confinement scale is the universal mass scale of light-front holography, previously extracted from spectroscopic data for light hadrons. With the Dirac and Pauli form factors normalized using the quark counting rules and the measured anomalous magnetic moments respectively, the masses of the quark…
A primary question in hadron physics is how the mass scale for hadrons consisting of light quarks, such as the proton, emerges from the QCD Lagrangian even in the limit of zero quark mass. If one requires the effective action which underlies the QCD Lagrangian to remain conformally invariant and extends the formalism of de Alfaro, Fubini and Furlan to light-front Hamiltonian theory, then a unique, color-confining potential with a mass parameter $κ$ emerges. The actual value of the parameter $κ$ is not set by the model - only ratios of hadron masses and other hadronic mass scales are predicted.…
A natural calculus for describing the bound-state structure of relativistic composite systems in quantum field theory is the light-front Fock expansion which encodes the properties of a hadrons in terms of a set of frame-independent n-particle wavefunctions. Light-front quantization in the doubly-transverse light-cone gauge has a number of remarkable advantages, including explicit unitarity, a physical Fock expansion, the absence of ghost degrees of freedom, and the decoupling properties needed to prove factorization theorems in high momentum transfer inclusive and exclusive reactions. A numbe…
A remarkable feature of QCD is that the mass scale which controls color confinement and hadron mass scales does not appear explicitly in the QCD Lagrangian. However, de Alfaro, Fubini, and Furlan have shown that a mass scale can appear in the equations of motion without affecting the conformal invariance of the action if one adds a term to the Hamiltonian proportional to the dilatation operator or the special conformal operator. Applying the same procedure to the light-front Hamiltonian leads to a unique confinement potential $κ^4 ζ^2$ for mesons, where $ζ$ is the LF radial variable conjugate …
The structure of the nucleon and the first radial excitation of the nucleon, the Roper, $N(1440)$, is studied within the formalism of Light-Front holography. The nucleon elastic form factors and $γ^\ast N \to N(1440)$ transition form factors are calculated under the assumption of the dominance of the valence quark degrees of freedom. Contrary to the previous studies, the bare parameters of the model associated with the valence quark are fixed by the empirical data for large momentum transfer ($Q^2$) assuming that the corrections to the three-quark picture (meson cloud contributions) are suppre…
We obtain the light-front wavefunctions for the nucleon in the valence quark Fock space from an effective Hamiltonian, which includes the transverse and longitudinal confinement and the one-gluon exchange interaction with fixed coupling. The wavefunctions are generated by solving the eigenvalue equation in a basis light-front quantization. Fitting the model parameters, the wavefunctions lead to good simultaneous description of electromagnetic form factors, radii, and parton distribution functions for the proton.
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…
Light-Front Hamiltonian theory provides a rigorous frame-independent framework for solving nonperturbative QCD. 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 equation, with an effective confining potential U which systematically incorporates the effects of higher quark and gluon Fock states. Remarkably, the potential U has a unique form of a harmonic oscillator potential if one requires that the chiral QCD action remains conformally invariant. A mass gap aris…
We find a correspondence between semiclassical gauge theories quantized on the light-front and a dual gravity model in anti-de Sitter (AdS) space, thus providing an initial approximation to QCD in its strongly coupled regime. This correspondence -- light-front holography -- leads to a light-front Hamiltonian and relativistic bound-state 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. Light-front holography also allows a precise mapping of transition amplitudes from AdS t…
We identify an invariant light-front coordinate $ζ$ 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 frame-independent 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. Light-front holography is a …
