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Light-Front Holographic QCD and Emerging Confinement
Abstract and Figures
In this Report we explore the remarkable connections between light-front
dynamics, its holographic mapping to gravity in a higher-dimensional anti-de
Sitter (AdS) space, and conformal quantum mechanics. This approach provides new
insights into the origin of a fundamental mass scale and the physics underlying
confinement dynamics in QCD in the limit of massless quarks. The result is a
relativistic light-front wave equation for arbitrary spin with an effective
confinement potential derived from a conformal action and its embedding in AdS
space. This equation allows for the computation of essential features of hadron
spectra in terms of a single scale. The light-front holographic methods
described here gives a precise interpretation of holographic variables and
quantities in AdS space in terms of light-front variables and quantum numbers.
This leads to a relation between the AdS wave functions and the boost-invariant
light-front wavefunctions describing the internal structure of hadronic
bound-states in physical space-time. The pion is massless and the excitation
spectra of relativistic light-quark meson and baryon bound states lie on linear
Regge trajectories with identical slopes in the radial and orbital quantum
numbers. In the light-front holographic approach described here currents are
expressed as an infinite sum of poles, and form factors as a product of poles.
At large the form factor incorporates the correct power-law fall-off for
hard scattering independent of the specific dynamics and is dictated by the
twist. At low the form factor leads to vector dominance. The approach is
also extended to include small quark masses. We briefly review in this Report
other holographic approaches to QCD, in particular top-down and bottom-up
models based on chiral symmetry breaking. We also include a discussion of open
problems and future applications.
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... Some kinesin motors can perform a large number of steps before detaching and are thus processive motors [38][39][40]. They move towards the plus ends of microtubules (anterograde direction) [41,42] with a strong preference for forward stepping over backward stepping. This means their direction is towards the cell periphery which is the plus end of microtubules' polarity [38,41]. ...
... They move towards the plus ends of microtubules (anterograde direction) [41,42] with a strong preference for forward stepping over backward stepping. This means their direction is towards the cell periphery which is the plus end of microtubules' polarity [38,41]. ...
We present a model to calculate the displacement and extension of deformable cellular cargo pulled by molecular motors stepping along cytoskeletal filaments. We consider the case of a single type of molecular motor and cytoskeletal filaments oriented in one dimension in opposite directions on either side of a cargo. We model a deformable cargo as a simple elastic spring. We simulate this tug-of-war simple exclusion process model using a Monte Carlo Gillespie algorithm and calculate the displacement and extension of the cargo for different configurations of motors and filaments. We apply our model to kinesin-1 motors on microtubules to investigate whether they are strong enough to translocate and deform the largest cellular cargo, the nucleus. We show that the extension caused by motors on a single microtubule saturates for larger numbers of motors but that the extension and displacement scales linearly with the number of microtubules. We also show how the binding and unbinding behaviors of molecular motors on microtubule filaments affect the nuclear deformation. Our modelling results correspond to experiments on cells treated with the drug kinesore, which is thought to increase rescue events resulting in more stable microtubules and more active kinesin-1 molecular motors bound to them. Both the experiments and our simulations result in nuclear deformation.
... The proton is modeled as a composite system with an active gluon and a spin-1 2 spectator, primarily composed of three valence quarks at low energies. The light-front wave functions (LFWFs) are constructed from two-particle effective wave functions of soft-wall AdS/QCD [107]. The model parameters are determined by fitting the unpolarized gluon PDF to the NNPDF3.0nlo ...
... Here, M and M s denote the masses of the proton and spectator, respectively. The function φðx; k 2 ⊥ Þ is a modified version of the soft-wall AdS/QCD wave function [105,107,111], modeled with the introduction of parameters a and b, ...
We calculate the gluon gravitational form factors (GFFs) of the proton using a light-front spectator model based on soft-wall anti–de Sitter (AdS)/quantum chromodynamics (QCD), where the active parton is a gluon. The model parameters are determined by fitting the unpolarized gluon distribution function to the 3.0nlo dataset. Subsequently, we predict the polarized gluon distribution, finding consistency with global analyses. Our predictions for the gluon GFFs show good agreement with recent lattice QCD simulations and experimental extractions. Using these gluon GFFs, we compute the contribution of the gluon to the proton mass and mechanical radii. We also analyze the gluonic contribution to the two-dimensional Galilean densities, including energy density, radial and tangential pressure, isotropic pressure, and pressure anisotropy of the proton.
Published by the American Physical Society 2025
... In addition to the renormalization scale μ r ambiguity, there are other sources of uncertainty, such as the NRQCD matrix element, the factorization scale μ Λ , the c-quark mass m c , and the value of α s ðM Z Þ. The factorization scale μ Λ uncertainty exists also for conformal theories, and it can be set by matching the perturbative prediction with the nonperturbative bound-state dynamics [52]. ...
The next-to-next-to-leading-order (NNLO) perturbative QCD (pQCD) predictions for both the decay width and the transition form factor in the η c → γ γ process, based on nonrelativistic QCD (NRQCD), deviate from precise experimental measurements. These significant discrepancies have cast doubt on the applicability of NRQCD to charmonium processes. In this paper, we analyze the η c → γ γ process by applying the principle of maximum conformality (PMC), a systematic method for eliminating renormalization scheme-and-scale ambiguities. The PMC renormalization scales are determined by absorbing the nonconformal β -terms that govern the behavior of the QCD running coupling via the renormalization group equation. We obtain the PMC scale Q ⋆ = 4.49 m c for the η c → γ γ decay width. Even after using the PMC method, the convergence of the pQCD series is still poor, which indicates the importance of uncalculated next-to-next-to-next-to-leading-order and higher-order terms. The resulting value for Γ η c → γ γ is in agreement with the Particle Data Group’s reported value of Γ η c → γ γ = 5.1 ± 0.4 keV within the bounds of uncertainties. Moreover, the transition form factor obtained using the PMC is also in good agreement with precise experimental measurements. The application of the PMC suggests a potential resolution to η c → γ γ puzzle and supports the applicability of NRQCD to charmonium processes.
Published by the American Physical Society 2025
... Various nonperturbative approaches have been developed to predict aspects of hadron spectra and to illuminate the partonic structures of hadrons [12][13][14][15]. Among these, basis light-front quantization (BLFQ) has emerged as a promising Hamiltonian framework for solving the nonperturbative dynamics of QCD [15]. ...
Within the basis light-front quantization framework, we compute the masses and light-front wave functions of the Λ b baryon and its isospin triplet counterparts Σ b + , Σ b 0 , and Σ b − using a light-front effective Hamiltonian in the leading Fock sector. These wave functions are obtained as eigenstates of the effective Hamiltonian, which incorporates the one-gluon exchange interaction with fixed coupling and a three-dimensional confinement potential. With the quark masses and the couplings as adjustable parameters, the computed masses are set within the experimental range. The resulting predictions for their electromagnetic properties align well with other theoretical calculations. Additionally, the parton distribution functions (PDFs) of these baryons are obtained for the first time, with gluon and sea quark distributions dynamically generated through QCD evolution of the valence quark PDFs.
Published by the American Physical Society 2025
... In Light-Front Holographic QCD, hadrons are described using light-front quantization, where dynamics are formulated at equal light-front time (x + = t + z). This choice simplifies the relativistic treatment of bound states by separating longitudinal and transverse degrees of freedom [3,5]. The holographic variable ζ, defined as ...
In this article, we propose a novel extension of Light-Front Holographic Quantum Chromodynamics (QCD) to study the effects of spin-orbit coupling on the baryon spectrum by introducing a flavor-dependent dynamical spin-orbit potential. This potential, modulated by the holographic coordinate and quark flavor, accounts for the mass hierarchy of quarks and the nonperturbative dynamics of confinement. By incorporating an exponentially decaying coupling that varies with the confinement scale, we capture the interplay between short-distance and long-distance spin-orbit interactions, particularly for heavy-light baryons. An optional coupling to holographic glueball fields further enriches the model, introducing nonperturbative QCD effects. The resulting modified light-front wave equation predicts flavor-dependent mass splittings and Regge trajectories, offering improved descriptions of both light and heavy baryon spectra. We discuss the implementation, parameter fitting, and testable predictions for experimental validation, particularly for heavy baryons observed at LHCb and Belle II. This approach bridges light and heavy quark dynamics, advancing the holographic modeling of baryon spectroscopy.
... Quantum Chromodynamics (QCD) governs the strong interactions of quarks and gluons, yet its nonperturbative behavior at low energies challenges the understanding of hadron spectroscopy and dynamics. Light-front holographic QCD (LFH QCD), leveraging the AdS/CFT correspondence, maps strongly coupled QCD in four-dimensional Minkowski space to a weakly coupled gravitational theory in five-dimensional anti-de Sitter (AdS) space [1]. This framework simplifies confinement modeling and reproduces key hadronic features, such as linear Regge trajectories. ...
In this article, we investigate the impact of a minimal length scale, introduced via the Generalized Uncertainty Principle (GUP), on meson form factors within light-front holographic QCD (). By incorporating GUP through deformed operators in the QCD Lagrangian, we derive a GUP-corrected light-front wave function (LFWF) that includes contributions from all Fock states, weighted by probabilities . The resulting form factors account for transitions between Fock states via coefficients , revealing a net positive -like correction driven by dominant positive coefficients (e.g., , ). This enhancement improves agreement with experimental pion form factor data. Our model is formulated to include all Fock states via the general summation over n , but numerical evaluations truncate to , sufficient for describing experimental data up to . Our findings suggest that minimal length effects amplify Fock state overlaps, offering insights into the interplay between quantum gravitational corrections and strong interaction dynamics. This generalized framework advances LFH QCD by capturing multi-parton contributions and paves the way for studying GUP effects in other hadronic systems.
... However, there is still a lack of information about this FF at a high Q 2 region. The pion vector FF has been investigated through lattice QCD simulations [42][43][44], lightfront holographic model (LFHM) [45], AdS/QCD [11], light-cone quark model (LCQM) [46], Nambu-Jona-Lasinio model (NJL) [47], contact interaction [48], etc. The kaon vector FF has been explored through experiments [39,40], lattice simulations [49,50] and in different theoretical models [46,51,52]. ...
We calculate the possible scalar, vector, and tensor form factors (FFs) for pion and kaon in the light-cone quark model (LCQM). These FFs are calculated from the leading and sub-leading twist generalized parton distribution functions (GPDs) of the pion and kaon. The vector and tensor FFs correspond to twist-2 GPDs, whereas the scalar FFs correspond to twist-3 scalar GPDs. We calculate the FFs from the GPDs quark-quark correlator and express them in the form of light-front wave functions (LFWFs). The behavior of these FFs was found to be in sync with experimental data, other model predictions, and lattice simulation results. We have also calculated the charge radii corresponding to different FFs and compared them with other models, lattice simulation results, and experimental data. The scalar radii of the pion and kaon of our model are found to be 0.528 and 0.409 fm, respectively.
... Notably, the predicted mass shifts for the pion and kaon align with their physical masses. These results were obtained by setting the scale parameter to κ ¼ 0.54 GeV, with light quark masses of m u=d ¼ 0.046 GeV and m s ¼ 0.357 GeV, which approach zero in the chiral limit [24]. ...
We show that the holographic Schrödinger equation of light-front chiral QCD, together with the ’t Hooft equation of ( 1 + 1 )-dimensional QCD in the large N c limit, can simultaneously describe the ϕ -meson mass spectroscopy as well as diffractive cross section. We compute the ϕ -meson diffractive cross section by utilizing its resulting light-front wave functions (LFWFs), in conjunction with the color glass condensate dipole scattering amplitude. Our predictions for the diffractive cross sections show good agreement with the existing experimental data from HERA at various energies from H1 and ZEUS Collaborations. Additionally, we show that the obtained ϕ -meson LFWFs effectively describe its various properties, including the decay constant, distribution amplitudes, electromagnetic form factors, charge radius, and magnetic and quadrupole moments.
Published by the American Physical Society 2025
Quark and gluon jets provide one of the best ways to probe the matter produced in ultrarelativistic high-energy collisions, from cold nuclear matter to hot quark-gluon plasma. In this work, we propose a unified framework for efficient quantum simulation of many-body dynamics using the ( 3 + 1 )-dimensional QCD Hamiltonian on the light front, particularly suited for studying the scattering of quark and gluon jets on nuclear matter in heavy-ion collisions. We describe scalable methods for mapping physical degrees of freedom onto qubits and for simulating in-medium jet evolution. We then validate our framework by implementing an algorithm that directly maps second-quantized Fock states onto qubits and uses Trotterized simulation for simulating time dynamics. Using a classical emulator, we investigate the evolution of quark and gluon jets with up to three particles in Fock states, extending prior studies. These calculations enable the study of key observables, including jet momentum broadening, particle production, and parton distribution functions.
Published by the American Physical Society 2025
Employing the world line spinning particle picture. We discuss the appearance of several different ‘gauges’ which we use to gain a deeper explanation of the Collective/Gravity identification. We discuss transformations and algebraic equivalences between them. For a bulk identification we develop a ‘gauge independent’ representation where all gauge constraints are eliminated. This ‘gauge reduction’ of Higher Spin Gravity demonstrates that the physical content of 4D AdS HS theory is represented by the dynamics of an unconstrained scalar field in 6d. It is in this gauge reduced form that HS Theory can be seen to be equivalent to a 3 + 3 dimensional bi-local collective representation of CFT3.
We discuss a holographic soft-wall model developed for the description of mesons and baryons with adjustable quantum numbers n, J, L, S. This approach is based on an action which describes hadrons with broken conformal invariance and which incorporates confinement through the presence of a background dilaton field. We show that in the case of the bound-state problem (hadronic mass spectrum) two versions of the model with a positive and negative dilaton profile are equivalent to each other by a special transformation of the bulk field. We also comment on recent works which discuss the dilaton sign in the context of soft-wall approaches.
Heavy ion collision experiments recreating the quark-gluon plasma that filled the microseconds-old universe have established that it is a nearly perfect liquid that flows with such minimal dissipation that it cannot be seen as made of particles. String theory provides a powerful toolbox for studying matter with such properties. This book provides a comprehensive introduction to gauge/string duality and its applications to the study of the thermal and transport properties of quark-gluon plasma, the dynamics of how it forms, the hydrodynamics of how it flows, and its response to probes including jets and quarkonium mesons. Calculations are discussed in the context of data from RHIC and LHC and results from finite temperature lattice QCD. The book is an ideal reference for students and researchers in string theory, quantum field theory, quantum many-body physics, heavy ion physics and lattice QCD. © J. Casalderrey-Solana, H. Liu, D. Mateos, K. Rajagopal and U. Wiedemann 2014.
We review recent progress in studying mesons within gauge/gravity duality, in the context of adding flavour degrees of freedom to generalizations of the AdS/CFT correspondence. Our main focus is on the "top-down approach" of considering models constructed within string theory. We explain the string-theoretical constructions in detail, aiming at non-specialists. These give rise to a new way of describing strongly coupled confining large-N gauge theories similar to large-N QCD. In particular, we consider gravity dual descriptions of spontaneous chiral symmetry breaking, and compare with lattice results. A further topic covered is the behaviour of flavour bound states in finite-temperature field theories dual to a gravity background involving a black hole. We also describe the "bottom up" phenomenological approach to mesons within AdS/QCD. Some previously unpublished results are also included.
We review the holographic correspondence between field theories and string/M theory, focusing on the relation between compactifications of string/M theory on Anti-de Sitter spaces and conformal field theories. We review the background for this correspondence and discuss its motivations and the evidence for its correctness. We describe the main results that have been derived from the correspondence in the regime that the field theory is approximated by classical or semiclassical gravity. We focus on the case of the N=4 supersymmetric gauge theory in four dimensions, but we discuss also field theories in other dimensions, conformal and non-conformal, with or without supersymmetry, and in particular the relation to QCD. We also discuss some implications for black hole physics.