  We develop a general theoretical framework for the description of
higher-twist baryon operators which makes maximal use of the conformal symmetry
of the QCD Lagrangian. The conformal operator basis is constructed for all
twists. The complete analysis of the one-loop renormalization of twist-4
operators is given. The evolution equation for three-quark operators of the
same chirality turns out to be completely integrable. The spectrum of anomalous
dimensions coincides in this case with the energy spectrum of the twist-4
subsector of the SU(2,2) Heisenberg spin chain. The results are applied to give
a general classification and calculate the scale dependence of subleading
twist-4 nucleon distribution amplitudes that are relevant for hard exclusive
reactions involving a helicity flip. In particular we find an all-order
expression (in conformal spin) for the contributions of geometric twist-3
operators to the (light-cone) twist-4 nucleon distribution amplitudes, which
are usually referred to as Wandzura-Wilczek terms.
