  Light front wave functions motivated by holographic constructions are used to
study Bloom-Gilman duality of deep inelastic scattering. Separate expressions
for structure functions in terms of quark and hadronic degrees of freedom are
presented, with a goal of relating the two expressions. A two-parton model is
defined and resonance transition form factors are computed using previously
derived light front wave functions. A new form of global duality is derived
from the valence quark-number sum rule. Using a complete set of hadronic states
is necessary for this new global duality to be achieved. Previous original work
does not provide such a set. This is remedied by amending the model to include
a longitudinal confining potential, and the resulting complete set is
sufficient to carry out the study of Bloom-Gilman duality. Expressions for
transition form factors are obtained and all are shown to fall asymptotically
as 1/Q2. The Feynman mechanism dominates the asymptotic behavior of the model.
These transition form factors are used to assess the validity of the global and
local duality sum rules, with the result that both neither are satisfied.
Evaluations of the hadronic expression for q(x,Q2) provide more details about
this lack. This result shows that the observed validity of both global and
local forms of duality for deep inelastic scattering must be related to a
feature of QCD that is deeper than completeness. Our simple present model
suggests a prediction that Bloom-Gilman duality would not be observed if deep
inelastic scattering experiments were to be made on the pion. The underlying
origin of the duality phenomenon in deep inelastic scattering is deeply buried
within the confinement aspects of QCD, and remains a mystery.
