  We study insertions of composite operators into Wilson loops in N=4
supersymmetric Yang-Mills theory in four dimensions. The loops follow a
circular or straight path and the composite insertions transform in the adjoint
representation of the gauge group. This provides a gauge invariant way to
define the correlator of non-singlet operators. Since the basic loop preserves
an SL(2,R) subgroup of the conformal group, we can assign a conformal dimension
to those insertions and calculate the corrections to the classical dimension in
perturbation theory. The calculation turns out to be very similar to that of
single-trace local operators and may also be expressed in terms of a
spin-chain. In this case the spin-chain is open and at one-loop order has
Neumann boundary conditions on the type of scalar insertions that we consider.
This system is integrable and we write the Bethe ansatz describing it. We
compare the spectrum in the limit of large angular momentum both in the dilute
gas approximation and the thermodynamic limit to the relevant string solution
in the BMN limit and in the full AdS_5 x S^5 metric and find agreement.
