O ( n ) Gauge Models and Self-Avoiding Random Surfaces in Three Dimensions

We show the exact equivalence between a self-avoiding random surface gas model with fluctuating topology on a three-dimensional lattice and a lattice gauge theory with local O ( n ) symmetry. n plays the role of the topological fugacity associated to the Euler characteristic of the surface. Using duality arguments a phase transition where the surface tension vanishes and the symmetry between the two sides of the surface is restored is found and is shown to belong to the Ising universality class.