Twisted bundles on noncommutativeT4and D-brane bound states

Abstract

We construct twisted quantum bundles and adjoint sections on noncommutative ${\mathbf{T}}^4,$ and investigate relevant D-brane bound states with non-Abelian backgrounds. We also show that the noncommutative ${\mathbf{T}}^4$ with non-Abelian backgrounds exhibits $\mathrm{SO}(4,4\mathrm{}|\mathbf{Z})$ duality and via this duality we get a Morita equivalent ${\mathbf{T}}^4$ on which only D0-branes exist. For a reducible non-Abelian background, the moduli space of D-brane bound states in type II string theory takes the form ${\prod }_a({\mathbf{T}}^4{)}^{q_a}{/S}_{q_a}.$