Phase Structures of U(2) Gauge Theory with $θ$-Term in 2 dimensions

Abstract

U(2) lattice gauge theory with $θ$-term in 2 space-time dimensions is investigated. It has non-Abelian real action and Abelian( U(1) type) imaginary action. The imaginary action is defined as the standard $θ$-term. As the effect of renormalization group (RG) transformation, non-Abelian imaginary action is induced. After many steps of RG transformation, non-Abelian part will die away. After several steps of RG transformations, renormalized action approaches so called heat kernel action. Phase transition is found at $θ=π$ only.