  Several approaches to quantum gravity (including the model of superplastic
vacuum; Diakonov tetrads emerging as the bilinear combinations of the fermionis
fields; $BF$-theories of gravity; and effective acoustic metric) suggest that
in general relativity the metric must have dimension 2, i.e.
$[g_{\mu\nu}]=1/[L]^2$, irrespective of the dimension of spacetime. This leads
to the "dimensionless physics" discussed in the review paper G.E. Volovik,
Dimensionless physics, JETP 132, 727 (2021). Here we continue to exploit this
unusual dimension of the metric.
