Threefold complementary approach to holographic QCD

Stanley J Brodsky,Guy F De Téramond,Hans Günter Dosch

doi:10.1016/j.physletb.2013.12.044

Abstract

A complementary approach, derived from (a) higher-dimensional anti-de Sitter (AdS) space, (b) light-front quantization and (c) the invariance properties of the full conformal group in one dimension leads to a nonperturbative relativistic light-front wave equation which incorporates essential spectroscopic and dynamical features of hadron physics. The fundamental conformal symmetry of the classical QCD Lagrangian in the limit of massless quarks is encoded in the resulting effective theory. The mass scale for confinement emerges from the isomorphism between the conformal group and SO(2,1). This scale appears in the light-front Hamiltonian by mapping to the evolution operator in the formalism of de Alfaro, Fubini and Furlan, which retains the conformal invariance of the action. Remarkably, the specific form of the confinement interaction and the corresponding modification of AdS space are uniquely determined in this procedure.

Highlights

One of the most interesting questions in hadron physics is the nature of the interaction which permanently confines quarks and gluons, the fundamental fields of QCD
The AdS/CFT correspondence between gravity on a higher-dimensional anti–de Sitter (AdS) space and conformal field theories (CFT) in physical space-time [1] is an explicit realization of the holographic principle, which postulates that a gravitational system may be equivalent to a non-gravitational system in one fewer dimension [2, 3]
The main result of this Letter is the unique determination of the confining potential from the underlying conformal symmetry of the classical QCD Lagrangian, incorporated in an effective one-dimensional light-front effective theory for QCD

Summary

Introduction

One of the most interesting questions in hadron physics is the nature of the interaction which permanently confines quarks and gluons, the fundamental fields of QCD. The mapping of the equations of motion [6] and the matching of the electromagnetic [7, 8] and gravitational [9] form factors in AdS space [10, 11] with the corresponding expressions derived from light-front quantization in physical space time is the central feature of the light-front holographic approach to hadronic physics. To a first semiclassical approximation, light-front QCD is formally equivalent to the equations of motion on a fixed gravitational background asymptotic to AdS5 In this semiclassical approach to AdS gravity, the confinement properties can be encoded in a dilaton profile φ(z) in AdS space which introduces a length scale in the AdS action and leads to conformal symmetry breaking, but its form is left largely unspecified. The model predicts hadronic light-front wavefunctions which underlie form factors [16] and other dynamical observables, as well as vector meson electroproduction [17]

Light-Front Dynamics

Conformal Quantum Mechanics

Connection to Light-Front Holographic QCD

Conclusions