ABSTRACT

We study the algebra of normal ordered and reparametrization invariant operators of the open bosonic string field theory. These, besides the Poincaré group generators, include the ghost number operator and two translationally invariant symmetric second-rank space-time tensors. The BRST operator of string field theory is the trace of the fermionic one, and the second is the BRST transform of the former. Their algebra closes only when certain Lorentz non-invariant projections over the fermionic tensor are taken. There are many inequivalent such algebras, corresponding to manifest Lorentz invariance in lower dimensions. Some of these contain, besides the Lorentz invariant BRST, another nilpotent operator. We provide an example where Lorentz invariance is manifest in 1 + 1 dimensions.

I recall that the first time Murray asked me to come and talk at Caltech sixteen years ago, the subject was one we both shared an interest in: covariant string field theory. After all these years, things have not changed so much as to force me to change the subject matter: Plus ça change, plus c'est la même chose. I recall Murray inquiring at the time as to the underlying principle behind string theory. His penetrating question is still valid and unanswered today.

In a series of publications, we set about to list normal-ordered operators which are invariant under complex reparametrizations. In open string field theory, these include familiar operators such as the ghost number operator, the Poincaré generators, and the BRST charge.