Surface operators and magnetic degrees of freedom in yang-mills theories

Magnetic degrees of freedom are manifested through violations of the Bianchi identities and associated with singular fields. Moreover, these singularities should not induce color nonconservation. We argue that the resolution of the constraint is that the singular fields, or defects are Abelian in nature. Recently proposed surface operators seem to represent a general solution to this constraint and can serve as a prototype of magnetic degrees of freedom. Some basic lattice observations, such as the Abelian dominance of the confining fields, are explained then as consequences of the original non-Abelian invariance. Generically, the properties of the two-dimensional defects associated with the surface operators are close to the predictions of the dual models for the magnetic D2 branes.