Algebra of reparametrization-invariant and normal-ordered operators in open string field theory

Abstract

Normal-ordered reparametrization invariant operators of the open bosonic string field theory include, besides the Poincaré group generators, the ghost number operator, and two translationally invariant symmetric second-rank space-time tensors, with the BRST operator as the trace of the fermionic one. We study their algebra, and find that it closes only when appropriate projections of the fermionic tensor are taken. There are three types of solutions. The first one contains the full Lorentz generatirs in 26 dimensions, the ghost number operator and the usual BRST charge. The second breaks Lorentz invariance down to SO(1, 1) ⊗ SO(24), contains inter alia a new nilpotent operator with cohomology made up of null states. The third class breaks the Lorentz group completely.