World Volume Noncommutativity versus Target Space Noncommutativity

Abstract

It is known that the noncommutativity of D-brane coordinate is responsible for describing the higher-dimensional D-branes in terms of more fundamental ones such as D-particles or D-instantons, while considering a noncommutative torus as a target space is conjectured to be equivalent to introducing the background antisymmetric tensor field in matrix models. In the present paper we clarify the dual nature of both descriptions. Namely the noncommutativity of conjugate momenta of the D-brane coordinates realizes the target space structure, whereas noncommutativity of the coordinates themselves realizes world volume structure. We explicitly construct a boundary state for the Dirichlet boundary condition where the string boundary is adhered to the D-brane on the noncommutative torus. There are non-trivial relations between the parameters appeared in the algebra of the coordinates and that of the momenta.

17 pages, LaTex, no figures

References in corpus (16)

• Noncommutative Open String and D-brane
• Morita equivalence and duality
• Noncommutative Geometry from D0-branes in a Background B-field
• Space-Time Uncertainty Principle and Conformal Symmetry in D-Particle Dynamics
• Noncommutative Gauge Theories in Matrix Theory
• Twisted Bundle On Quantum Torus and BPS States in Matrix Theory
• Review of Matrix Theory
• Towards a Noncommutative Geometric Approach to Matrix Compactification
• Gauge Bundles and Born-Infeld on the Noncommutative Torus
• p-branes from (p-2)-branes in the Bosonic String Theory
• BPS states on noncommutative tori and duality
• Super Yang-Mills on the Noncomutative Torus
• Comments on Supersymmetric Yang-Mills Theory on a Noncommutative Torus
• Algebraic treatment of compactification on noncommutative tori
• A Note on the BPS Spectrum of the Matrix Model
• Orientifolds of Matrix theory and Noncommutative Geometry

Cited by in corpus (12)

• D-branes and Deformation Quantization
• Event shapes in e+e- annihilation and deep inelastic scattering
• Formation of Spherical D2-brane from Multiple D0-branes
• Canonical Quantization of Open String and Noncommutative Geometry
• Witten's Open String Field Theory in Constant B-Field Background
• Energy-momentum Tensors in Matrix Theory and in Noncommutative Gauge Theories
• Twisted Bundles on Noncommutative $T^4$ and D-brane Bound States
• Boundary States in B-Field Background
• Noncommutativities of D-branes and $\theta$-changing Degrees of Freedom in D-brane Matrix Models
• A Note on the Path Integral Representation of the Boundary State of D-brane
• Time-Delay at Higher Genus in High-Energy Open String Scattering
• Relations between Non-Commutative and Commutative Spacetime