Renormalizable parameters of the sine-Gordon model

TL;DR

This paper analyzes the phase structure of the two-dimensional sine-Gordon model using renormalization group flow, revealing novel universality features and addressing contradictions in its effective potential behavior.

Contribution

It reconstructs the phase structure via RG flow, highlighting the role of the Maxwell-cut and universality, and discusses implications for higher-dimensional gauge theories.

Findings

Renormalization group flow clarifies phase structure.

Maxwell-cut leads to strong universality.

Effective potential triviality does not contradict phase structure.

Abstract

The well-known phase structure of the two-dimensional sine-Gordon model is reconstructed by means of its renormalization group flow, the study of the sensitivity of the dynamics on microscopic parameters. Such an analysis resolves the apparent contradiction between the phase structure and the triviality of the effective potential in either phases, provides a case where usual classification of operators based on the linearization of the scaling relation around a fixed point is not available and shows that the Maxwell-cut generates an unusually strong universality at long distances. Possible analogies with four-dimensional Yang-Mills theories are mentioned, too.