  We investigate the entanglement structure of the continuous multi-scale
entanglement renormalization ansatz (cMERA) [Haegeman et al., Phys. Rev. Lett.,
110, 100402 (2013)] for ground states of quantum field theories (QFTs). The
cMERA, proposed as an extension to QFTs of the lattice MERA, is defined
directly in the continuum but is nevertheless naturally equipped with a
short-distance scale $1/\Lambda$ that acts as a UV regulator for quantum
fluctuations. We consider the simplified setting of Gaussian cMERA for free
QFTs, where explicit calculations can be performed. For relativistic free
massless bosonic and fermionic QFTs in both 1+1 and 2+1 spacetime dimensions,
we show that the cMERA state indeed displays no UV divergences in two-point
correlation functions or entanglement entropy, in sharp contrast with the exact
ground states.
