Hadron Spectroscopy and Wavefunctions in QCD and the AdS/CFT Correspondence

Abstract

Nonperturbative effects in QCD at finite temperature and density Phys. Part. Nucl. 30, 223 (1999) Condition on the symmetry-breaking solution of the Schwinger-Dyson equation J. Math. Phys. 38, 6119 (1997) Covariant algebraic calculation of the oneloop effective potential in nonAbelian gauge theory and a new approach to stability problem Abstract. The AdS/CFT correspondence has led to important insights into the properties of quantum chromodynamics even though QCD is a broken conformal theory. We have recently shown how a holographic model based on a truncated AdS space can be used to obtain the hadronic spectrum of light qq qqq and gg bound states. Specific hadrons are identified by the correspondence of string modes with the dimension of the interpolating operator of the hadron's valence Fock state, including orbital angular momentum excitations. The predicted mass spectrum is linear M ∝ L at high orbital angular momentum, in contrast to the quadratic dependence M 2 ∝ L found in the description of spinning strings. Since only one parameter, the QCD scale Λ QCD , is introduced, the agreement with the pattern of physical states is remarkable. In particular, the ratio of ∆ to nucleon trajectories is determined by the ratio of zeros of Bessel functions. The light-front quantization of gauge theories in light-cone gauge provides a frame-independent wavefunction representation of relativistic bound states, simple forms for current matrix elements, explicit unitarity, and a trivial vacuum. The light-front Fock-state wavefunctions encode the bound state properties of hadrons in terms of their quark and gluon degrees of freedom at the amplitude level. One can also use the extended AdS/CFT space-time theory to obtain a model for hadronic light-front wavefunctions, thus providing a relativistic description of hadrons in QCD at the amplitude level. The model wavefunctions display confinement at large inter-quark separation and conformal symmetry at short distances. In particular, the scaling and conformal properties of the LFWFs at high relative momenta agree with perturbative QCD. These AdS/CFT model wavefunctions could be used as an initial ansatz for a variational treatment of the light-front QCD Hamiltonian. We also show how hadron form factors in both the space-like and time-like regions can be predicted.

AdS/CFT and Light-Front QCD

“…The fundamental equations of AdS/CFT for mesons have the appearance of a radial Schrödinger Coulomb equation, but they are relativistic, covariant, and analytically tractable. The eigenvalues of the AdS/CFT equations provide a good description of the meson and baryon spectra for light quarks [44,81,111,112], and its eigensolutions provide a remarkably simple but realistic model of their valence wavefunctions. One can also derive analogous equations for baryons composed of massless quarks using a Dirac matrix representation for the baryon system [16].…”