Conformal Aspects of QCD

Theoretical and phenomenological evidence is now accumulating that the QCD coupling becomes constant at small virtuality; i.e., α_s(Q²) develops an infrared fixed point in contradiction to the usual assumption of singular growth in the infrared. For example, the hadronic decays of the τ lepton can be used to determine the effective charge α _τ ( {m_τ ² ,} ; ) for a hypothetical τ-lepton with mass in the range 0 < m_τ' < m_τ. The τ decay data at low mass scales indicates that the effective charge freezes at a value of s = m_τ ² of order 1 GeV² with a magnitude α_τ 0.9 ± 0.1. The near-constant behavior of effective couplings suggests that QCD can be approximated as a conformal theory even at relatively small momentum transfer and why there are no significant running coupling corrections to quark counting rules for exclusive processes. The AdS/CFT correspondence of large N_C supergravity theory in higher-dimensional anti-de Sitter space with supersymmetric QCD in 4-dimensional space-time also has interesting implications for hadron phenomenology in the conformal limit, including an all-orders demonstration of counting rules for exclusive processes and light-front wavefunctions. The utility of light-front quantization and light-front Fock wavefunctions for analyzing non-perturbative QCD and representing the dynamics of QCD bound states is also discussed.