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

Abstract

Character expansion developed in real space renormalization group (RSRG)\napproach is applied to U(1) lattice gauge theory with $\\th$-term in 2\ndimensions. Topological charge distribution $P(Q)$ is shown to be of Gaussian\nform at any $\\b$(inverse coupling constant). The partition function $Z(\\th)$ at\nlarge volume is shown to be given by the elliptic theta function. It provides\nthe information of the zeros of partition function as an analytic function of\n$\\ze= e^{i \\th}$ ($\\th$ = theta parameter). These partition function zeros lead\nto the phase transition at $\\th=\\pi$. Analytical results will be compared with\nthe MC simulation results. In MC simulation, we adopt (i)``set method" and\n(ii)``trial function method".\n