Phase Structure of ZN -Gauge Theory with θ-Term in 2-Dimensions

phase structure fer 2-dimensions, ZN lattice gauge theory with θ-term will be discussed on the basis of character expansion method developed in Real Space Renormalization Group (RSRG) approach. The action with 0-term in Euclidean space is written as Σp (-s+iv) where β is real action and iv is the imaginary action induced by 0-term. Flows of renoriualized coupling constant are analyzed. For a given critical imaginary bare coupling, γbe, renormalized flows for real and imaginary coupling converge to a finite values. This means that the system is in deconfinement at this values γbe. For each Ny there are N phase transition. By increasing γbe7*, the N phase transition are repeated. The model is shown to possess an infinite number of phase transition corresponding to θ = (2mo + ι) π (mo integer). For other values of γb the system is in the deconfinement phase