Gauge Bundles and Born-Infeld on the Noncommutative Torus

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.

22 pages, LaTeX2e. Small errors corrected

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• Canonical Quantization of Open String and Noncommutative Geometry
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• BPS states on noncommutative tori and duality
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• T-Duality and Ramond-Ramond Backgrounds in the Matrix Model
• Ramond-Ramond Couplings of Noncommutative D-branes
• Morita Duality and Large-N Limits
• Compactified D=11 Supermembranes and Symplectic Non-Commutative Gauge Theories
• Aspects of Gauge Theory on Commutative and Noncommutative Tori
• Open Wilson Lines and Group Theory of Noncommutative Yang-Mills Theory in Two Dimensions
• Moduli spaces of maximally supersymmetric solutions on noncommutative tori and noncommutative orbifolds
• A Note on the BPS Spectrum of the Matrix Model
• On Central Charges and Hamiltonians for 0-brane dynamics
• Compactification of M(atrix) theory on noncommutative toroidal orbifolds
• The BRS invariance of noncommutative U(N) Yang-Mills theory at the one-loop level
• Topology of Born-Infeld-AdS Black Hole Phase Transitions: Bulk and CFT Sides
• D-branes, Symplectomorphisms and Noncommutative Gauge Theories
• Comments on the Morita Equivalence
• 1/4-BPS states on noncommutative tori
• World Volume Noncommutativity versus Target Space Noncommutativity
• Nahm gauge fields for the torus
• Constructions of Non Commutative Instantons on $T^4$ and $K_3$
• On the short-distance structure of irrational non-commutative gauge theories
• CP^n Model on Fuzzy Sphere
• Twisted Bundles on Noncommutative $T^4$ and D-brane Bound States
• Generalized Fuzzy Torus and its Modular Properties
• Noncommutative K3 Surfaces
• Noncommutative Super Yang-Mills Theories with 8 Supercharges and Brane Configurations
• Dualities in Quantum Hall System and Noncommutative Chern-Simons Theory
• The Matrix model and the non-commutative geometry of the supermembrane
• Theta functions on Noncommutative T^4
• Matrix Theory Compactification on Noncommutative $T^4/Z_2$
• N-Point Deformation of Algebraic K3 Surfaces
• The Concept of a Noncommutative Riemann Surface
• Twisted Conformal Field Theories and Morita equivalence
• Noncommutative Geometry and Twisted Little-String Theories
• Compactified NCOS and duality
• Noncommutative fermions and Morita equivalence
• Paired quantum Hall states on noncommutative two-tori
• Dissipative quantum mechanics and Kondo-like impurities on noncommutative two-tori