  The representation theory of a conformal net is a unitary modular tensor
category. It is captured by the bimodule category of the Jones-Wassermann
subfactor. In this paper, we construct multi-interval Jones-Wassermann
subfactors for unitary modular tensor categories. We prove that these
subfactors are self-dual. It generalizes and categorifies the self-duality of
finite abelian groups and we call it modular self-duality.
