  We formulate a universal characterization of the many-particle quantum
entanglement in the ground state of a topologically ordered two-dimensional
medium with a mass gap. We consider a disk in the plane, with a smooth boundary
of length L, large compared to the correlation length. In the ground state, by
tracing out all degrees of freedom in the exterior of the disk, we obtain a
marginal density operator \rho for the degrees of freedom in the interior. The
von Neumann entropy S(\rho) of this density operator, a measure of the
entanglement of the interior and exterior variables, has the form S(\rho)=
\alpha L -\gamma + ..., where the ellipsis represents terms that vanish in the
limit L\to\infty. The coefficient \alpha, arising from short wavelength modes
localized near the boundary, is nonuniversal and ultraviolet divergent, but
-\gamma is a universal additive constant characterizing a global feature of the
entanglement in the ground state. Using topological quantum field theory
methods, we derive a formula for \gamma in terms of properties of the
superselection sectors of the medium.
