Noncommutative SO(n) and Sp(n) gauge theories

We study the generalization of noncommutative gauge theories to the case of orthogonal and symplectic groups. We find out that this is possible, since we are allowed to define orthogonal and symplectic subgroups of noncommuta tive unitary gauge transformations even though the gauge potentials and gau ge transformations are not valued in the orthogonal and symplectic subalgeb ras of the Lie algebra of antihermitean matrices. Our construction relies o n an anti-automorphism of the basic noncommutative algebra of functions whi ch generalizes the charge conjugation operator of ordinary field theory. We show that the corresponding noncommutative picture from low energy string theory is obtained via orientifold projection in the presence of a non-triv ial NSNS B field. (C) 2000 Elsevier Science B.V. All rights reserved.