RECURSION RELATIONS IN CLOSED STRING FIELD THEORY

The logical framework of closed string field theory is discussed. Such field theory requires the existence of vertices, namely, sets of surfaces, which appear to be generators of an algebra of Riemann surfaces. The consistency conditions on these vertices take the form of geometrical recursion relations. Conformal field theories yield representations of the vertices and allow the construction of string actions. The recursion relations turn into the Batalin-Vilkovisky master equation.