Closed string field theory

Abstract

A gauge invariant cubic action describing bosonic closed string field theory is constructed. The gauge symmetries include local spacetime diffeomorphisms. The conventional closed string spectrum and trilinear couplings are reproduced after spontaneous symmetry breaking. The action L is constructed from the usual “open string” field of ghost number minus one half. It is given by the associator of the string field product which is non-vanishing because of associativity anomalies. L does not describe open string propagation because open string states association and can thereby be shifted away. A field theory of closed and open strings can be obtained by adding to L the cubic open string action.