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 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.

A. ~b d u r r a h m a n~ and F. Ant6nWe give the general form of the vertex corresponding to the interaction of an arbitrary number of strings. The technique employed relies on the "comma" representation of string field theory where string fields and interactions are represented as matrices and operations between them such as multiplication and trace. The general formulation presented here shows that the interaction vertex of N strings, for any arbitrary N , is given as a function of particular combinations of matrices corresponding to the change of representation between the full string and the half string degrees of freedom. PACS numberk): 11.25.Sq

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