Topological anomalies in the n dependence of the n-states Potts lattice gauge theory

Abstract

We demonstrate that there is an unexpected n dependence in the topological representation of the n-states gauge Potts model as a theory of random surfaces. Our results show that there are some inherent difficulties in regarding n as a continuous parameter. In particular, we point out some difficulties in constructing plaquette percolation as the n → 1 limit of the n-states gauge Potts model and in setting up a 1/ n expansion. While we find anomalies in the Wilson-loop expectation already in three dimensions, for the free energy the occur only in four or more dimensions. Related difficulties might appear in the Z n clock and the pure SU( n) lattice gauge theories.