Mr. Gaberdiel et B. Zwiebach, TENSOR CONSTRUCTIONS OF OPEN STRING THEORIES .2. VECTOR-BUNDLES, D-BRANES AND ORIENTIFOLD GROUPS, Physics letters. Section B, 410(2-4), 1997, pp. 151-159
A generalized Chan-Paton construction is presented which is analogous
to the tensor product of vector bundles. To this end open string theor
ies are considered where the space of states decomposes into sectors w
hose product is described by a semigroup. The cyclicity properties of
the open string theory are used to prove that the relevant semigroups
are direct unions of Brandt semigroups. The known classification of Br
andt semigroups then implies that all such theories have the structure
of a theory with Dirichlet-branes. We also describe the structure of
an arbitrary orientifold group, and show that the truncation to the in
variant subspace defines a consistent open string theory. Finally, we
analyze the possible orientifold projections of a theory with several
kinds of branes. (C) 1997 Elsevier Science B.V.