  We make an exact field theoretical computation of the conformal anomaly for
two-dimensional submanifold observables. By including a scalar field in the
definition for the Wilson surface, as appropriate for a spontaneously broken
A_1 theory, we get a conformal anomaly which is such that N times it is equal
to the anomaly that was computed in hep-th/9901021 in the large N limit and
which relied on the AdS-CFT correspondence. We also show how the spherical
surface observable can be expressed as a conformal anomaly.
