Twisted Bundle On Quantum Torus and BPS States in Matrix Theory

Abstract

Following the recent work of Connes, Douglas and Schwarz, we study the M(atrix) model compactified on a torus with a background of the three-form field. This model is given by a super Yang-Mills theory on a quantum torus. To consider twisted gauge field configurations, we construct twisted U(n) bundles on the quantum torus as a deformation of its classical counterpart. By properly taking into account membranes winding around the light-cone direction, we derive from the M(atrix) model the BPS spectrum which respects the full SL(2,Z)*SL(2,Z) U-duality in M theory.

14 pages, no figure. minor modification made

References in corpus (6)

• Why is the Matrix Model Correct?
• Compactification in the Lightlike Limit
• Noncommutative Gauge Theories in Matrix Theory
• Why Matrix Theory is Hard
• Towards a Noncommutative Geometric Approach to Matrix Compactification
• Comments on Supersymmetric Yang-Mills Theory on a Noncommutative Torus

Cited by in corpus (52)

• Quantum Field Theory on Noncommutative Spaces
• Noncommutative Open String and D-brane
• Noncommutative Geometry From Strings and Branes
• Introduction to M(atrix) theory and noncommutative geometry
• Introduction to M(atrix) theory and noncommutative geometry, Part II
• Dirac Quantization of Open Strings and Noncommutativity in Branes
• Emergent Gravity from Noncommutative Spacetime
• Quantum Mechanics on the Noncommutative Torus
• Noncommutative Gauge Theories in Matrix Theory
• String Geometry and the Noncommutative Torus
• Dualities of the Matrix Model from T-Duality of the Type II String
• Morita equivalence and T-duality (or B versus $\Theta$)
• Gauge Bundles and Born-Infeld on the Noncommutative Torus
• Noncommutative D-Brane in Non-Constant NS-NS B Field Background
• Massive IIA String Theory and Matrix Theory Compactification
• Matrix theory origins of non-geometric fluxes
• Tachyon Condensation on Noncommutative Torus
• BPS states on noncommutative tori and duality
• The CP(n) Model on Noncommutative Plane
• Lorentzian Lie (3-)algebra and toroidal compactification of M/string theory
• T-Duality and Ramond-Ramond Backgrounds in the Matrix Model
• On noncommutative Nahm transform
• Super Yang-Mills on the Noncomutative Torus
• Compactified D=11 Supermembranes and Symplectic Non-Commutative Gauge Theories
• A Note on the BPS Spectrum of the Matrix Model
• D-branes, Symplectomorphisms and Noncommutative Gauge Theories
• SL(2,Z) symmetries, Supermembranes and Symplectic Torus Bundles
• Twisted Bundle on Noncommutative Space and U(1) Instanton
• World Volume Noncommutativity versus Target Space Noncommutativity
• On the short-distance structure of irrational non-commutative gauge theories
• Twisted Bundles on Noncommutative $T^4$ and D-brane Bound States
• Lowest Landau level theory of the bosonic Jain states
• Duality Rotations and BPS Monopoles with Space and Time Noncommutativity
• Homological mirror symmetry on noncommutative two-tori
• Gauge Fields on Tori and T-duality
• Kronecker foliation, D1-branes and Morita equivalence of Noncommutative two-tori
• D0-branes in an H-field Background and Noncommutative Geometry
• Star product formula of theta functions
• Theta functions on Noncommutative T^4
• Noncommutative Deformation of Instantons
• Non-commutativity, Zero modes and D-brane Geometry
• The Concept of a Noncommutative Riemann Surface
• Bogomolny equations for vortices in the noncommutative torus
• Orientifolds of Matrix theory and Noncommutative Geometry
• Matrix Compactification On Orientifolds
• Compactified NCOS and duality
• Global Seiberg-Witten maps for U(n)-bundles on tori and T-duality
• Noncommutativities of D-branes and $\theta$-changing Degrees of Freedom in D-brane Matrix Models
• Noncommutative Geometry and Twisted Little-String Theories
• T-Duality Group for Open String Theory
• Non commutative geometry for outsiders; an elementary introduction to motivations and tools
• (m,n)-Strings In IIB Matrix Model