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

TL;DR

This paper uses real space renormalization group methods to analyze the phase structure of 2D U(1) gauge theory with a theta-term, revealing a phase transition at theta equals pi and confinement behavior elsewhere.

Contribution

It introduces a real space RG analysis of the U(1) gauge theory with a theta-term, identifying fixed points and phase transitions not previously characterized.

Findings

Flows converge to a single trajectory regardless of initial couplings

System is in confinement phase for theta not equal to pi

A phase transition occurs at theta equals pi

Abstract

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