Comment on "A structural test for the conformal invariance of the critical 3d Ising model" by S. Meneses, S. Rychkov, J. M. Viana Parente Lopes and P. Yvernay. arXiv:1802.02319

TL;DR

This paper refutes a recent challenge to the proof that scale invariance implies conformal invariance in the 3D Ising model, clarifying misunderstandings and correcting a calculation mistake in the critique.

Contribution

It provides a rebuttal to the critique of the conformal invariance proof and corrects a specific computational error in the previous critique.

Findings

The critique's arguments are invalidated.

The original proof of conformal invariance remains robust.

A mistake in the critique's one-loop calculation is identified and corrected.

Abstract

In a recent preprint [ArXiv 1802.02319], Meneses et al. challenge our proof that scale invariance implies conformal invariance for the three-dimensional Ising model [B. Delamotte, M. Tissier and N. Wschebor, Phys. Rev. E 93 (2016), 012144.]. We refute their arguments. We also point out a mistake in their one-loop calculation of the dimension of the vector operator $V_\mu$ of lowest dimension which is not a total derivative.