  We study the two-loop dilatation operator in the noncompact SL(2) sector of
QCD and supersymmetric Yang-Mills theories with N=1,2,4 supercharges. The
analysis is performed for Wilson operators built from three quark/gaugino
fields of the same helicity belonging to the fundamental/adjoint representation
of the SU(3)/SU(N_c) gauge group and involving an arbitrary number of covariant
derivatives projected onto the light-cone. To one-loop order, the dilatation
operator inherits the conformal symmetry of the classical theory and is given
in the multi-color limit by a local Hamiltonian of the Heisenberg magnet with
the spin operators being generators of the collinear subgroup of full
(super)conformal group. Starting from two loops, the dilatation operator
depends on the representation of the gauge group and, in addition, receives
corrections stemming from the violation of the conformal symmetry. We compute
its eigenspectrum and demonstrate that to two-loop order integrability survives
the conformal symmetry breaking in the aforementioned gauge theories, but it is
violated in QCD by the contribution of nonplanar diagrams. In SYM theories with
extended supersymmetry, the N-dependence of the two-loop dilatation operator
can be factorized (modulo an additive normalization constant) into a
multiplicative c-number. This property makes the eigenspectrum of the two-loop
dilatation operator alike in all gauge theories including the maximally
supersymmetric theory. Our analysis suggests that integrability is only tied to
the planar limit and it is sensitive neither to conformal symmetry nor
supersymmetry.
