  String representations of the Wilson loop are constructed in the
SU(N)-version of compact QED in three and four dimensions. This is done exactly
in the case of the fundamental Wilson loop and in the large-N limit in the case
of the adjoint Wilson loop. Using for concreteness the three-dimensional
fundamental case, it is demonstrated how the resulting SU(N)-generalization of
the so-called theory of confining strings can be obtained in various ways. In
its weak-field limit (corresponding to the limit of low monopole densities),
this theory enables one to fix the value of the string tension, which cannot be
fixed when deduced from the mean magnetic field inside a flat contour (the
derivation of this field is also presented). Moreover, the obtained theory
enables one to find also the coupling constants of terms in the expansion of
the nonlocal string effective action, which are higher in the derivatives than
the Nambu-Goto term (some of these terms vanish at the flat surface). In the
four-dimensional case with the theta-term, the critical values of the
theta-parameter, at which the problem of crumpling of large world sheets might
be solved, are found in both the fundamental case and in the large-N limit of
the adjoint case. These values are only accessible provided the electric
coupling constant is larger than a certain value, in accordance with the known
fact that confinement in the four-dimensional compact QED holds in the
strong-coupling regime.
