Tensor constructions of open string theories (I) Foundations
Abstract
The possible tensor constructions of open string theories are analyzed from first principles. To this end the algebraic framework of open string field theory is clarified, including the role of the homotopy associative A _{∞} algebra, the odd symplectic structure, cyclicity, star conjugation, and twist. It is also shown that two string theories are offshell equivalent if the corresponding homotopy associative algebras are homotopy equivalent in a strict sense. It is demonstrated that a homotopy associative star algebra with a compatible even bilinear form can be attached to an open string theory. If this algebra does not have a spacetime interpretation, positivity and the existence of a conserved ghost number require that its cohomology is at degree zero, and that it has the structure of a direct sum of full matrix algebras. The resulting string theory is shown to be physically equivalent to a string theory with a familiar open string gauge group.
 Publication:

Nuclear Physics B
 Pub Date:
 February 1997
 DOI:
 10.1016/S05503213(97)005804
 arXiv:
 arXiv:hepth/9705038
 Bibcode:
 1997NuPhB.505..569G
 Keywords:

 High Energy Physics  Theory
 EPrint:
 62 pages, LaTeX