Tensor Constructions of Open String Theories I: Foundations

Details Tensor Constructions of Open String Theories I: Foundations Tensor Constructions of Open String Theories I: Foundations

1997-05-06

arxiv.org/abs/hep-th/9705038v1

Nucl.Phys. B505 (1997) 569-624

Physics

High Energy Physics

High Energy Physics - Theory

62 pages, LaTeX

Scientific paper

10.1016/S0550-3213(97)00580-4

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_\infty algebra, the odd symplectic structure, cyclicity, star conjugation, and twist. It is also shown that two string theories are off-shell 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.

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