Character Expansion, Zeros of Partition Function and θ-Term in U(1) Gauge Theory

Ahmed S. HASSAN, Masahiro IMACHI * , Norimasa TSUZUKI** Department of Physics, Kyushu University, Fukuoka 812-81, JAPAN Hiroshi YONEYAMA *** Department of Physics, Saga University, Saga 840, JAPAN Abstract Character expansion developed in real space renormalization group (RSRG) approach is applied to U(1) lattice gauge theory with θ-term in 2 dimensions. Topological charge distribution P (Q) is shown to be of Gaussian form at any β(inverse coupling constant). The partition function Z(θ) at large volume is shown to be given by the elliptic theta function. It provides the information of the zeros of partition function as an analytic function of ζ = e (θ = theta parameter). These partition function zeros lead to the phase transition at θ = π. Analytical results will be compared with the MC simulation results. In MC simulation, we adopt (i)“set method” and (ii)“trial function method”.