  The recent claim by Grebenev et al. [J. Phys. A: Math. Theor. 50, 435502
(2017)] that the inviscid 2D Lundgren-Monin-Novikov (LMN) equations on a zero
vorticity characteristic naturally would reveal local conformal invariance when
only analyzing these by means of a classical Lie-group symmetry approach, is
invalid and will be refuted in the present comment. To note is that within this
comment the (possible) existence of conformal invariance in 2D turbulence is
not questioned, only the conclusion as is given in Grebenev et al. (2017) and
their approach how this invariance was derived is what is being criticized and
refuted herein. In fact, the algebraic derivation for conformal invariance of
the 2D LMN vorticity equations in Grebenev et al. (2017) is flawed. A key
constraint of the LMN equations has been wrongly transformed. Providing the
correct transformation instead will lead to a breaking of the proclaimed
conformal group. The corrected version of Grebenev et al. (2017) just leads to
a globally constant scaling in the fields and not to a local one as claimed. In
consequence, since in Grebenev et al. (2017) only the first equation within the
infinite and unclosed LMN chain is considered, also different Lie-group
infinitesimals for the one- and two-point probability density functions (PDFs)
will result from this correction, replacing thus the misleading ones proposed.
