LightFront Quantization and AdS/QCD: An Overview
Abstract
We give an overview of the lightfront holographic approach to strongly coupled QCD, whereby a confining gauge theory, quantized on the light front, is mapped to a higherdimensional 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 {yields} 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 offshell 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 {zeta} which measures the separation of the partons within the hadron at equal lightfront time. Alternatively, one can start from the gravity side by studying the propagation ofmore »
 Authors:
 Publication Date:
 Research Org.:
 SLAC National Accelerator Lab., Menlo Park, CA (United States)
 Sponsoring Org.:
 USDOE
 OSTI Identifier:
 1022479
 Report Number(s):
 SLACPUB14393
arXiv:1103.1100; TRN: US1104238
 DOE Contract Number:
 AC0276SF00515
 Resource Type:
 Conference
 Resource Relation:
 Journal Name: J.Phys.Conf.Ser.287:012007,2011; Conference: InvitedThe XIV Mexican School on Particles and Fields, of Morelia, Michoacan, Mexico, 11/8/201011/12/2010
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ANGULAR MOMENTUM; BOUND STATE; CONFINEMENT; EDUCATIONAL FACILITIES; EQUATIONS OF MOTION; GEOMETRY; HADRONS; HAMILTONIANS; HOLOGRAPHY; MODIFICATIONS; QUANTIZATION; QUANTUM CHROMODYNAMICS; QUARKS; SEMICLASSICAL APPROXIMATION; SPACETIME; TRANSITION AMPLITUDES; PhenomenologyHEP, TheoryHEP,HEPPH, HEPTH
Citation Formats
de Teramond, Guy F., /Costa Rica U., Brodsky, Stanley J., and /SLAC /Stanford U., Phys. Dept. LightFront Quantization and AdS/QCD: An Overview. United States: N. p., 2011.
Web.
de Teramond, Guy F., /Costa Rica U., Brodsky, Stanley J., & /SLAC /Stanford U., Phys. Dept. LightFront Quantization and AdS/QCD: An Overview. United States.
de Teramond, Guy F., /Costa Rica U., Brodsky, Stanley J., and /SLAC /Stanford U., Phys. Dept. 2011.
"LightFront Quantization and AdS/QCD: An Overview". United States.
doi:. https://www.osti.gov/servlets/purl/1022479.
@article{osti_1022479,
title = {LightFront Quantization and AdS/QCD: An Overview},
author = {de Teramond, Guy F. and /Costa Rica U. and Brodsky, Stanley J. and /SLAC /Stanford U., Phys. Dept.},
abstractNote = {We give an overview of the lightfront holographic approach to strongly coupled QCD, whereby a confining gauge theory, quantized on the light front, is mapped to a higherdimensional 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 {yields} 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 offshell 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 {zeta} which measures the separation of the partons within the hadron at equal lightfront 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 {zeta}. Lightfront holography thus allows a precise mapping of transition amplitudes from AdS to physical spacetime. The internal structure of hadrons is explicitly introduced and the angular momentum of the constituents plays a key role.},
doi = {},
journal = {J.Phys.Conf.Ser.287:012007,2011},
number = ,
volume = ,
place = {United States},
year = 2011,
month = 8
}

Lightfront wavefunctions provide a frameindependent representation of hadrons in terms of their physical quark and gluon degrees of freedom. The lightfront Hamiltonian formalism provides new nonperturbative methods for obtaining the QCD spectrum and eigensolutions, including resolvant methods, variational techniques, and discretized lightfront quantization. A new method for quantizing gauge theories in lightcone gauge using Dirac brackets to implement constraints is presented. In the case of the electroweak theory, this method of lightfront quantization leads to a unitary and renormalizable theory of massive gauge particles, automatically incorporating the Lorentz and 't Hooft conditions as well as the Goldstone boson equivalence theorem.more »

LightFront Quantization Approach to the Gauge Gravity Correspondence and Hadron Spectroscopy
We find a correspondence between semiclassical QCD quantized on the lightfront and a dual gravity model in antide Sitter (AdS) space, thus providing an initial approximation to QCD in its strongly coupled regime. This correspondence  lightfront holography  leads to a lightfront Hamiltonian and relativistic boundstate wave equations that are functions of an invariant impact variable {zeta} which measures the separation of the quark and gluonic constituents within hadrons at equal lightfront time. The eigenvalues of the resulting lightfront Schrodinger and Dirac equations are consistent with the observed light meson and baryon spectrum, and the eigenmodes provide the lightfrontmore » 
Electron Anomalous Magnetic Moment in Basis LightFront Quantization Approach
We apply the Basis LightFront Quantization (BLFQ) approach to the Hamiltonian field theory of Quantum Electrodynamics (QED) in free space. We solve for the mass eigenstates corresponding to an electron interacting with a single photon in lightfront gauge. Based on the resulting nonperturbative ground state lightfront amplitude we evaluate the electron anomalous magnetic moment. The numerical results from extrapolating to the infinite basis limit reproduce the perturbative Schwinger result with relative deviation less than 1.2%. We report significant improvements over previous works including the development of analytic methods for evaluating the vertex matrix elements of QED.