DERIVING THE FOUR-STRING AND OPEN-CLOSED STRING INTERACTIONS FROM GEOMETRIC STRING FIELD THEORY

One of the baffling questions concerning the covariant open string field theory is why there are two distinct BRST theories and why the four-string interaction appears in one version but not the other. We solve this mystery by showing that both theories are gauge-fixed versions of a higher gauge theory, called the geometric string field theory, with a new field, a string vierbein [Formula: see text], which allows us to gauge the string length and σ-parametrization. By fixing the gauge, we can derive the “endpoint gauge” (the covariantized light cone gauge), the “midpoint gauge” of Witten, or the “interpolating gauge” with arbitrary string lengths. We show explicitly that the four-string interaction is a gauge artifact of the geometric theory (the counterpart of the four-fermion instantaneous Coulomb term of QED). By choosing the interpolating gauge, we produce a new class of four-string interactions which smoothly interpolate between the endpoint gauge and the midpoint gauge (where it vanishes). Similarly, we can extract the closed string as a bound state of the open string, which appears in the endpoint gauge but vanishes in the midpoint gauge. Thus, the four-string and open-closed string interactions do not have to be added to the action as long as the string vierbein is included.