Has the Goldstone theorem been revisited?

TL;DR

This paper clarifies misconceptions about the Goldstone theorem, demonstrating that recent claims of a loophole are invalid and reaffirming the theorem's validity in scalar theories.

Contribution

The paper refutes a recent claim of a loophole in the Goldstone theorem, reaffirming its validity and addressing misconceptions about covariance and scalar operators.

Findings

The proposed loophole is not valid under covariance.

The counterexample involving scalar operators is ill-defined.

The Goldstone theorem remains valid in the analyzed context.

Abstract

A recent paper (arXiv:1404.5619) claimed the presence of a loophole in the current-algebra proof of Goldstone Theorem. The enforcing of manifest covariance would lead to contradictory results also in scalar theory. We show that the argument proposed is not in contradiction with covariance, thus not invalidating the theorem. Moreover, the counterexample proposed of a scalar operator with a non-zero vacuum expectation value in an unbroken theory is ill-defined.