A Gauge Invariant Action Containing Both Open and Closed String Fields

Abstract

An interesting feature of the covariant open string field theory is that the closed string appears as a bound state of the open string.),2) This suggests the existence in open string field theory of a larger gauge symmetry which includes general coordinate transformation. Motivated by this, Hata and N ojiri proposed a new transformation on the open string field) with closed string functional parameter in the formulation of string field theory proposed in Refs. 4) and 5). The structure of the transformation and its algebra are those of stringy general coordinate transformation known in the closed string field theory.5) The gauge invariant open string action is, however, invariant under only the global part of the transformation.. It seems to contradict the existence of the closed string pole in open string one-loop amplitude which is computed from the BRS invariant action. On the basis of a covariant string field theory constructed by Kyoto group,4),5) we propose a new covariant action which contains both open and closed string fields and· is invariant not only under the gauge transformation in the usual open string theory but also under stringy general coordinate transformation. Since the action contains only the interaction terms as in case of the pre-geometrical cubic action in Ref. 6) or Ref. 7), it is background independent. The kinetic term is generated through field condensation of the fields. We investigate the form of the action after the field condensation correspondIng to the flat background. The relation between the new action and the BRS invariant action of Ref. 4) is also discussed in this paper. Before constructing the new action, we define several operations on string fields. First we' define the transition from an open ·string field (j) to a closed string field (denoted by «(j)) and that from a closed string field A to an open string field [A] as follows:*) .