  Calculations of the entanglement entropy of a spatial region in continuum
quantum field theory require boundary conditions on the fields at the
fictitious boundary of the region. These boundary conditions impact the
treatment of the zero modes of the fields and their contribution to the
entanglement entropy. We explore this issue in the simplest example, the c=1
compact-boson conformal field theory in 1+1 dimensions. We consider three
different types of boundary conditions: spatial Neumann, temporal Neumann, and
Dirichlet. We argue that the first two are well motivated, and show that they
lead to the same result for the Renyi entropies as well as the entanglement
entropy, including a constant term that corresponds to the Affleck-Ludwig
boundary entropy. The last set of boundary conditions is less well motivated,
and leads to a different value of the constant term. The two values are related
by a duality transformation on the compact boson. We also verify some of our
results with heat-kernel methods.
