Why are there two BRST string field theories?

Abstract

One of the mysteries of string field theory is why there are two distinct BRST field theories. We solve this puzzle by (1) explicitly constructing a geometric vertex that smoothly interpolates between the other theories, (2) proving that this geometric vertex links the other two by a one-dimensional reparametrization, (3) proving that both BRST theories are thus gauge-fixed versions of a higher, geometric field theory. The geometric theory also explains the origin of the baffling four-string interaction, which now emerges as a gauge artifact, the counterpart of the four-fermion instantaneous Coulomb term of QED.