Conformal anomaly of Wilson surface observables - a field theoretical computation

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 A1 theory, we get a conformal anomaly which is such that 2N 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. (author)