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We explore new connections between the fields and local observables in twodimensional chiral conformal field theory. We show that in a broad class ofexamples, the von Neumann algebras of local observables (a conformal net) canbe obtained from the fields (a unitary vertex operator algebra) via acontinuous geometric interpolation procedure involving Graeme Segal'sfunctorial definition of conformal field theory. In particular, we constructconformal nets from these unitary vertex operator algebras by showing that'geometrically mollified' versions of the fields yield bounded, local operatorson the Hilbert space completion of the vertex algebra. This work is inspired byHenriques' picture of conformal nets arising from degenerate Riemann surfaces.

Geometric realization of algebraic conformal field theories