Twisted Bundles on Noncommutative $T^4$ and D-brane Bound States

TL;DR

This paper constructs twisted quantum bundles on noncommutative T^4, explores D-brane bound states with non-Abelian backgrounds, and reveals duality relations leading to Morita equivalent tori with simplified D-brane configurations.

Contribution

It introduces a framework for twisted bundles on noncommutative T^4 and analyzes their duality properties and D-brane bound states with non-Abelian backgrounds.

Findings

Noncommutative T^4 with non-Abelian backgrounds exhibits SO(4,4|Z) duality.

Morita equivalent T^4 with only D0-branes is obtained via duality.

Moduli space of D-brane bound states has a product form involving symmetric groups.

Abstract

We construct twisted quantum bundles and adjoint sections on noncommutative $T^4$, and investigate relevant D-brane bound states with non-Abelian backgrounds. We also show that the noncommutative $T^4$ with non-Abelian backgrounds exhibits SO$(4,4|Z)$ duality and via this duality we get a Morita equivalent $T^4$ 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 $\prod_a (T^4)^{q_a}/S_{q_a}$.