  On the lattice, a renormalization group (RG) flow for two-dimensional
partition functions expressed as a tensor network can be obtained using the
tensor network renormalization (TNR) algorithm [G. Evenbly, G. Vidal, Phys.
Rev. Lett. 115 (18), 180405 (2015)]. In this work we explain how to extend TNR
to field theories in the continuum. First, a short-distance length scale
$1/\Lambda$ is introduced in the continuum partition function by smearing the
fields. The resulting object is still defined in the continuum but has no
fluctuations at distances shorter than $1/\Lambda$. An infinitesimal
coarse-graining step is then generated by the combined action of a $rescaling$
operator $L$ and a $disentangling$ operator $K$ that implements a quasi-local
field redefinition. As demonstrated for a free boson in two dimensions,
continuous TNR exactly preserves translation and rotation symmetries and can
generate a proper RG flow. Moreover, from a critical fixed point of this RG
flow one can then extract the conformal data of the underlying conformal field
theory.
