In this paper, the authors say that the trace of the energy-momentum tensor has to vanish to allow for the existence of conserved dilatation or scaling currents, as defined on p 10, Eq(22)
$$ \Theta^{\mu} = x_{\nu} \Theta^{\mu\nu} + \Sigma^\mu.$$
$\Theta^{\mu\nu}$ is the energy-momentum tensor and $\Sigma^\mu = d_{\phi}\pi_i^{\mu}\phi^i$ is the internal part.
This fact is just mentioned and I dont understand why this has to be the case, so can somebody explain it to me?