Remarks about an "exact" RG theory of Goldstone modes

TL;DR

This paper critically examines a purported exact RG theory for Goldstone modes in the O(n>1) phi^4 model, revealing mathematical errors that invalidate its predictions of Gaussian behavior in the long-wave limit.

Contribution

The paper identifies fundamental mathematical errors in a claimed exact RG theory, challenging its predictions about Goldstone mode behavior.

Findings

The RG theory's predictions of Gaussian behavior are incorrect.

Mathematical errors undermine the theory's validity.

Discussion of alternative perturbative approaches.

Abstract

A renormalization group (RG) theory of Goldstone mode singularities in the O(n>1)-symmetric phi^4 model is discussed. This perturbative RG theory is claimed to be asymptotically exact, as regards the long-wave limit of the correlation functions, where it predicts a purely Gaussian behavior of the transverse correlation function. However, we show that the results of this theory are incorrect, and the Gaussian behavior originates from a rough error in mathematics. Other relevant perturbative theories are discussed, as well.