Restrictions on Gauge Parameters in Open String Field Theory

A. Iwazaki
1987 Progress of theoretical physics  
We show in Witten's formulation of open strings that the axiom, fQA=O, does not hold for A with component local fields decaying slowly at infinity. It follows that we must restrict the function space of gauge parameters to keep gauge invariance of the formulation. Consequently, a gauge, eoA = ° cannot necessarily be achieved. Field theories 1 ),2) of strings have recently attracted much attention. It is expected that the field theories of strings enable us to obtain useful information on
more » ... formation on nonperturbative aspects such as symmetry breaking, compactification, or uniqueness of a theory, in a unification model given by the string theory. One of the most convincing field theories of open strings is Witten's theory.2),3) It has been indicated 4 ) that the theory generates a modular invariant perturbative expansions of scattering amplitudes. Hence, it is natural that we analyze the details of its structure to go beyond the perturbation theory (recently an anomaly in Witten's axiom has been pointed out,S) but we do not address to the anomaly). In this paper we show that an axiom, fQA=O, does not necessarily hold. Consequently, the function space of gauge parameters is so restricted that there exist field configurations which cannot be transformed to ones satisfying a desirable gauge. We also examine the validity of the gauge fixing condition, CoA = 0, used in recent papers. 4 ),6),7) Witten's field theory2) of open strings is described with the action,
doi:10.1143/ptp.78.990 fatcat:vp6xjp4xnzasfljsjl65qixg6y