Real Space Renormalization Group Analysis of U(1)-Gauge Theory with theta-term in 2 Dimensions

Abstract

U(1) lattice gauge theory with $θ$-term is investigated by real space renormalization group approach. Flows of renormalized coupling constants are analyzed. For each $θ$, renormalization flows converge to a single trajectory irrespective of bare coupling constants of real action. For $θ\not= π$ the system is in the confinement phase controlled by an infrared fixed point. We found a phase transition at $θ= π$. Imaginary part of the action given by $θ$-term stays fixed under renormalization group transformations leading to deconfinement.