Abstract
The statistical mechanics of polymer molecules subject to topological constraints is formulated. In particular, the problem of two polymer loops topologically linked is studied in the limit when one of the loops is allowed to fill a macroscopic volume at a finite density. The authors show that this problem can be recast as a local gauge invariant field theory in the usual limit that the number of components goes to zero. The gauge invariance is a direct consequence of the fact that topological entanglements imposed on the system are conserved.