  I give some scalar field theory calculations on a d-dimensional lune of
arbitrary angle, evaluating, numerically, the effective action which is
expressed as a simple quadrature, for conformal coupling. Using this, the
entanglement and Renyi entropies are computed. Massive fields are also
considered and a renormalisation to make the (one-loop) effective action vanish
for infinite mass is suggested and used, not entirely successfully. However a
universal coefficient is derived from the large mass expansion.
  From the deformation of the corresponding lune result, I conjecture that the
effective action on all manifolds with a simple conical singularity has an
extremum when the singularity disappears.
  For the round sphere, I show how to convert the quadrature form of the
conformal Laplacian determinant into the more usual sum of Riemann zeta
functions (and log2).
