  In 1+1-dimensional conformal field theory, the thermal state on a circle is
related to a certain quotient of the vacuum on a line. We explain how to take
this quotient in the MERA tensor network representation of the vacuum and
confirm the validity of the construction in the critical Ising model. This
result suggests that the tensors comprising MERA can be interpreted as
performing local scale transformations, so that adding or removing them
emulates conformal maps. In this sense, the optimized MERA recovers local
conformal invariance, which is explicitly broken by the choice of lattice. Our
discussion also informs the dialogue between tensor networks and holographic
duality.
