Operator approach to purely cubic string field theory

Abstract

A formulation of Witten's field theory of interacting open bosonic strings has been given based on a purely cubic action principle; however, the construction involves formal arguments which could in principle be invalidated by anomalies. We establish that the potential quantum anomalies cancel identically, making use of the recently developed operator formalism of Witten's theory. We first give an operator construction of the BRST current j( σ), determining its proper normal-ordering prescription through the requirement that j( σ) itself be BRST invariant. (As a by-product, we also obtain its anomalous current-current anticommutator.) The anomaly calculation then involves numerous nontrivial identities for the Neumann coefficients occurring in the oscillator form of the vertex, and gives a stringent consistency check upon the form of j( σ). Finally, we comment upon further issues to be resolved in pursuing this approach to string field theory.