TENSOR CONSTRUCTIONS OF OPEN STRING THEORIES .1. FOUNDATIONS

The possible tensor constructions of open string theories are analyzed from first principles. To this end the algebraic framework of open st ring field theory is clarified, including the role of the homotopy ass ociative A(infinity) algebra, the odd symplectic structure, cyclicity, star conjugation, and twist. It is also shown that two string theorie s are off-shell equivalent if the corresponding homotopy associative a lgebras are homotopy equivalent in a strict sense. It is demonstrated that a homotopy associative star algebra with a compatible even biline ar form can be attached to an open string theory. If this algebra does not have a space-time interpretation, positivity and the existence of a conserved ghost number require that its cohomology is at degree zer o, and that it has the structure of a direct sum of full matrix algebr as. The resulting string theory is shown to be physically equivalent t o a string theory with a familiar open string gauge group. (C) 1997 El sevier Science B.V.