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In this letter we present an operator formalism for Closed String Field Theory based on closed half-strings. Our results indicate that the restricted polyhedra of the classical non-polynomial string field theory, can be represented as traces of infinite matrices, with operator insertions that reparametrise the half-strings.

The comma representation of interacting string field theory is further elucidated. The proof that Witten's vertex solves the comma overlap equations is established. In this representation, the associativity of the star algebra is seen to hold. The relationship of the symmetry K in the standard formulation of Witten's string field theory to that in the comma theory is discussed. ͓S0556-2821͑98͒07618-8͔

The Coulomb gas formalism is employed to construct contour integral representations of two-point correlation functions on the torus for the N=1 superconformal unitary discrete series, characterized by the single integer p. (For the particular case of the tricritical Ising model, these include the energy and vacancy density operators.) Modular and monodromy properties of the superconformal blocks are examined, and the generalization to superconformal theories of Verlinde’s results on modular transformations and the fusion algebra are discussed in some detail. For p odd the relevant modular matrix is (with respect to a particular basis) symmetric and unitary, as in ordinary rational conformal theory. However, for p even, there appears to be an obstruction due to the Ramond vacuum state.