Gauge Bundles and Born-Infeld on the Noncommutative Torus

TL;DR

This paper constructs and analyzes noncommutative gauge bundles on higher-dimensional tori, explores their duality properties, and applies these results to string theory, demonstrating T-duality invariance of the Born-Infeld action.

Contribution

It provides explicit constructions of non-abelian gauge bundles with fluxes on noncommutative tori and examines their Morita equivalence and duality transformations.

Findings

Explicit noncommutative gauge bundle constructions with fluxes

Demonstration of T-duality invariance of the Born-Infeld action

Discussion of U-duality invariant BPS mass formula

Abstract

In this paper, we describe non-abelian gauge bundles with magnetic and electric fluxes on higher dimensional noncommutative tori. We give an explicit construction of a large class of bundles with nonzero magnetic 't Hooft fluxes. We discuss Morita equivalence 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 fluctuations, is manifestly invariant under the T-duality group SO(4,4;Z). The U-duality invariant BPS mass-formula is discussed shortly. We comment on a discrepancy of this result with that of a recent calculation.