We revisit the role of loop and surface operators as order parameters for
gapped phases of four-dimensional gauge theories. We show that in some cases
surface operators are confined, and that this fact can be used to distinguish
phases which are not distinguished by the Wilson-'t Hooft criterion. The
long-distance behavior of loop and surface operators which are neither confined
nor screened is controlled by a 4d TQFT. We construct these TQFTs for phases
which are characterized by the presence of electrically and/or magnetically
charged condensates. Interestingly, the TQFT describing a phase with a
nonabelian monopole condensate is based on the theory of nonabelian gerbes. We
also show that in phases with a dyonic condensate the low-energy theta-angle is
quantized.Comment: 10 pages, late
