  Instanton contributions to the anomalous dimensions of gauge-invariant
composite operators in the N=4 supersymmetric SU(N) Yang-Mills theory are
studied in the one-instanton sector. Independent sets of scalar operators of
bare dimension 2, 3, 4 and 5 are constructed in all the allowed representations
of the SU(4) R-symmetry group and their two-point functions are computed in the
semiclassical approximation. Analysing the moduli space integrals the sectors
in which the scaling dimensions receive non-perturbative contributions are
identified. The requirement that the integrations over the fermionic collective
coordinates which arise in the instanton background are saturated leads to
non-renormalisation properties for a large class of operators.
Instanton-induced corrections to the scaling dimensions are found only for
dimension 4 SU(4) singlets and for dimension 5 operators in the representation
[0,1,0] of SU(4). In many cases the non-renormalisation results are argued to
be specific to operators of small dimension, but for some special sectors it is
shown that they are valid for arbitrary dimension. Comments are also made on
the implications of the results on the form of the instanton contributions to
the dilation operator of the theory and on the possibility of realising its
action on the instanton moduli space.
