http://cds.cern.ch/record/326993/files/9705477.pdf

Quantum chromodynamics and other field theories on the light cone

https://scholarworks.wm.edu/cgi/viewcontent.cgi?article=1956&context=aspubs

Light-front holographic QCD and emerging confinement

A matrix model of an asymptotically free theory with a bound state is solved using a perturbative similarity renormalization group for hamiltonians. An effective hamiltonian with a small width, calculated including the first three terms in the perturbative expansion, is projected on a small set of effective basis states. The resulting small hamiltonian matrix is diagonalized and the exact bound state energy is obtained with accuracy of order 10%. Then, a brief description and an elementary illustration are given for a related light-front Fock space operator method which aims at carrying out analogous steps for hamiltonians of QCD and other theories.

Renormalization of Hamiltonians.

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 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 wave functions describing the internal structure of hadronic bound states in physical space-time. The pion is massless in the chiral limit 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 $q^2$ 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 $q^2$ 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.

/pdf/light-front-holographic-qcd-and-emerging-confinement-79pnst41uw.pdf

Light-Front Holographic QCD and Emerging Confinement

Explicitly covariant light-front dynamics and relativistic few-body systems

In this work the determination of low-energy bound states in quantum chromodynamics is recast so that it is linked to a weak-coupling problem. This allows one to approach the solution with the same techniques which solve quantum electrodynamics: namely, a combination of weak-coupling diagrams and many-body quantum mechanics. The key to eliminating necessarily nonperturbative effects is the use of a bare Hamiltonian in which quarks and gluons have nonzero constituent masses rather than the zero masses of the current picture. The use of constituent masses cuts off the growth of the running coupling constant and makes it possible that the running coupling never leaves the perturbative domain. For stabilization purposes an artificial potential is added to the Hamiltonian, but with a coefficient that vanishes at the physical value of the coupling constant. The weak-coupling approach potentially reconciles the simplicity of the constituent quark model with the complexities of quantum chromodynamics. The penalty for achieving this perturbative picture is the necessity of formulating the dynamics of QCD in light-front coordinates and of dealing with the complexities of renormalization which such a formulation entails. We describe the renormalization process first using a qualitative phase space cell analysis, and we then set up a precise similarity renormalization scheme with cutoffs on constituent momenta and exhibit calculations to second order. We outline further computations that remain to be carried out. There is an initial nonperturbative but nonrelativistic calculation of the hadronic masses that determines the artificial potential, with binding energies required to be fourth order in the coupling as in QED. Next there is a calculation of the leading radiative corrections to these masses which requires our renormalization program. Then the real struggle of finding the right extensions to perturbation theory to study the strong-coupling behavior of bound states can begin.

Nonperturbative QCD: A weak-coupling treatment on the light front

Recent work on the derivation of the nucleon-nucleon potential from interacting solitons in the Skyrme model is reviewed. A general introduction to the Skyrme and extended Lagrangians is given and the quantization of the solitons of these theories is described. Results from various studies of the two-skyrmion interaction using ansatze, time-dependent numerical simulations and time-independent constrained calculations are discussed. Improvements which include intermediate deltas in these latter calculations are presented and the resulting nucleon-nucleon interaction compares well with phenomenological potentials.

Timothy S. Walhout

Papers

Nonperturbative QCD: A weak-coupling treatment on the light front

From skyrmions to the nucleon-nucleon potential