  The overlap formulation is applied to calculate the chiral determinant on a
two-dimensional torus with twisted boundary conditions. We evaluate first the
continuum overlap, which is convergent and well-defined, and yields the correct
string theory result for both the real and imaginary parts of the effective
action. We then show that the lattice version of the overlap gives the
continuum overlap results in the limit when the lattice spacing tends to zero,
and that the subleading terms in that limit are irrelevant.
