Gaussian Effective Potential Analysis of Sinh(Sine)-Gordon Models by New Regularization-Renormalization Scheme

TL;DR

This paper applies a new regularization-renormalization scheme to analyze sine-Gordon and sinh-Gordon models using Gaussian effective potential, avoiding divergences and revealing differences from previous results, especially in three dimensions.

Contribution

It introduces a divergence-free analysis of sine-Gordon models using a novel regularization scheme within the Gaussian effective potential framework, extending understanding to higher dimensions.

Findings

Exact agreement with previous results in D=1,2

Disagreement with prior work in D=3, showing non-trivial sinh-Gordon model

Identification of poles in the running coupling constant indicating critical points

Abstract

Using the new regularization and renormalization scheme recently proposed by Yang and used by Ni et al, we analyse the sine-Gordon and sinh-Gordon models within the framework of Gaussian effective potential in D+1 dimensions. Our analysis suffers no divergence and so does not suffer from the manipulational obscurities in the conventional analysis of divergent integrals. Our main conclusions agree exactly with those of Ingermanson for D=1,2 but disagree for D=3: the D=3 sinh(sine)-Gordon model is non-trivial. Furthermore, our analysis shows that for D=1,2, the running coupling constant (RCC)has poles for sine-Gordon model($\gamma^2<0$) and the sinh-Gordon model ($\gamma^2>0$) has a possible critical point $\gamma^2_c$ while for D=3, the RCC has poles for both $\gamma^2>0$ and $\gamma^2<0$.