Gauge bundles and Born-Infeld on the noncommutative torus

Abstract

In this paper, we describe non-abelian gauge bundles with magnetic and electric uxes on higher dimensional noncomm utative tori. We give an explicit construction of a large class of bundles with nonzero magnetic 't Hooft uxes. W e discuss Morita equiv alence between these bundles. The action of the duality is worked out in detail for the four-torus. As an application, we discuss Born-Infeld on this torus, as a description of compactified string theory. We show that the resulting theory, including the uctuations, is manifestly invariant under the T-duality group SO(4; 4; Z ). The U-duality invariant BPS mass-formula is discussed shortly. W e commen t on a discrepancy of this result with that of a recent calculation.