  We study the scaling behavior of the entanglement entropy of two dimensional
conformal quantum critical systems, i.e. systems with scale invariant wave
functions. They include two-dimensional generalized quantum dimer models on
bipartite lattices and quantum loop models, as well as the quantum Lifshitz
model and related gauge theories. We show that, under quite general conditions,
the entanglement entropy of a large and simply connected sub-system of an
infinite system with a smooth boundary has a universal finite contribution, as
well as scale-invariant terms for special geometries. The universal finite
contribution to the entanglement entropy is computable in terms of the
properties of the conformal structure of the wave function of these quantum
critical systems. The calculation of the universal term reduces to a problem in
boundary conformal field theory.
