Morita equivalence and duality

Abstract

It was shown by Connes, Douglas, Schwarz[1] that one can compactify M(atrix) theory on noncommutative torus. We prove that compactifications on Morita equivalent tori are physically equivalent. This statement can be considered as a generalization of non-classical duality conjectured in [1] for two-dimensional tori.

References in corpus (10)

• Instantons on noncommutative R^4, and (2,0) superconformal six dimensional theory
• Noncommutative Geometry from D0-branes in a Background B-field
• M-Theory and U-duality on T^d with Gauge Backgrounds
• Noncommutative Gauge Theories in Matrix Theory
• Towards a Noncommutative Geometric Approach to Matrix Compactification
• Non-local Field Theories and the Non-commutative Torus
• Comments on Supersymmetric Yang-Mills Theory on a Noncommutative Torus
• Algebraic treatment of compactification on noncommutative tori
• A Matrix Model for Heterotic $Spin(32)/Z_2$ and Type I String Theory
• A Note on Six-Dimensional Gauge Theories

Cited by in corpus (124)

• Noncommutative Field Theory
• Quantum Field Theory on Noncommutative Spaces
• U-duality and M-Theory
• Introduction to M(atrix) theory and noncommutative geometry, Part II
• Introduction to M(atrix) theory and noncommutative geometry
• The One-loop UV Divergent Structure of U(1) Yang-Mills Theory on Noncommutative R^4
• Non(anti)commutative Superspace
• Nonperturbative Dynamics of Noncommutative Gauge Theory
• Metrics on states from actions of compact groups
• Dipoles, Twists and Noncommutative Gauge Theory
• A Noncommutative M-Theory Five-brane
• Noncommutative D=4 gravity coupled to fermions
• Real Multiplication and noncommutative geometry
• A Non-Perturbative Study of Gauge Theory on a Non-Commutative Plane
• String Geometry and the Noncommutative Torus
• Dualities of the Matrix Model from T-Duality of the Type II String
• Overview Of K-Theory Applied To Strings
• Phase diagram and dispersion relation of the non-commutative λϕ^{4} model in d=3
• The characteristic classes of Morita equivalent star products on symplectic manifolds
• Morita equivalence and T-duality (or B versus $\Theta$)
• Gauge Bundles and Born-Infeld on the Noncommutative Torus
• *-Trek III: The Search for Ramond-Ramond Couplings
• Quantum mechanics on noncommutative Riemann surfaces
• BPS states on noncommutative tori and duality
• S-Duality, Deconstruction and Confinement for a Marginal Deformation of N=4 SUSY Yang-Mills
• The CP(n) Model on Noncommutative Plane
• Perturbative Instabilities on the Non-Commutative Torus, Morita Duality and Twisted Boundary Conditions
• Critical fields on the M5-brane and noncommutative open strings
• T-Duality and Ramond-Ramond Backgrounds in the Matrix Model
• Ramond-Ramond Couplings of Noncommutative D-branes
• Noncommutative Solitons on Orbifolds
• p-p' System with B-field, Branes at Angles and Noncommutative Geometry
• Super Yang-Mills on the Noncomutative Torus
• Poisson geometry and Morita equivalence
• Morita Duality and Large-N Limits
• Aspects of Gauge Theory on Commutative and Noncommutative Tori
• A Note on the BPS Spectrum of the Matrix Model
• Moduli spaces of maximally supersymmetric solutions on noncommutative tori and noncommutative orbifolds
• Semi-Flatland
• Compactification of M(atrix) theory on noncommutative toroidal orbifolds
• The BRS invariance of noncommutative U(N) Yang-Mills theory at the one-loop level
• Noncommutative line bundle and Morita equivalence
• Lectures on Two-Dimensional Noncommutative Gauge Theory 2: Quantization
• Non-Commutative Geometry from Strings
• Comments on the Morita Equivalence
• Regularization of Non-commutative SYM by Orbifolds with Discrete Torsion and SL(2,Z) Duality
• Noncommutativity and the Motion of D${}_p$-brane along Itself
• Morita Duality and Noncommutative Wilson Loops in Two Dimensions
• On matrix models for anomalous dimensions of super Yang-Mills theory
• Gromov-Hausdorff Distance for Quantum Metric Spaces
• 1/4-BPS states on noncommutative tori
• Classical Solutions of the TEK Model and Noncommutative Instantons in Two Dimensions
• Wilson line correlators in two-dimensional noncommutative Yang-Mills theory
• Noncommutative supergeometry, duality and deformations
• World Volume Noncommutativity versus Target Space Noncommutativity
• CP^n Model on Fuzzy Sphere
• Constructions of Non Commutative Instantons on $T^4$ and $K_3$
• Gauge theories on noncommutative spaces
• On the short-distance structure of irrational non-commutative gauge theories
• A reconstruction theorem for Connes-Landi deformations of commutative spectral triples
• Twisted Bundles on Noncommutative $T^4$ and D-brane Bound States
• Semiclassical Geometry of Quantum Line Bundles and Morita Equivalence of Star Products
• Harmonic analysis approach to Gromov--Hausdorff convergence for noncommutative tori
• Discrete Noncommutative Gauge Theory
• Supersymmetry algebra and BPS states of super Yang-Mills theories on noncommutative tori
• Duality Rotations and BPS Monopoles with Space and Time Noncommutativity
• Differential and complex geometry of two-dimensional noncommutative tori
• Non-commutative compactifications and elliptic curves
• Spin(p+1,p+1) Covariant Dp-brane Bound States
• Dualities in Quantum Hall System and Noncommutative Chern-Simons Theory
• Gauge-Invariant Resummation Formalism and Unitarity in Non-Commutative QED
• Topological T-Duality for Twisted Tori
• Homological mirror symmetry on noncommutative two-tori
• T-duality of non-commutative gauge theories
• Kronecker foliation, D1-branes and Morita equivalence of Noncommutative two-tori
• Exercising in K-theory: Brane Condensation without Tachyon
• Theta-functions on noncommutative tori
• Dual Non-Lorentzian Backgrounds for Matrix Theories
• A note on the topological order of noncommutative Hall fluids
• Duality in non-commutative gauge theories as a non-perturbative Seiberg-Witten map
• Matrix Theory Compactification on Noncommutative $T^4/Z_2$
• Noncommutative supergeometry and duality
• Poisson Chern-Simons Gauge Theory
• Gauge Invariance and Noncommutativity
• On Duality Rotations in Light-Like Noncommutative Electromagnetism
• A bicategorical approach to Morita equivalence for rings and von Neumann algebras
• Noncommutative Geometry, Strings and Duality
• Line Bundles over Quantum Tori
• Strong Coupling Phenomena on the Noncommutative Plane
• Reduced Models and Noncommutative Gauge Theories
• Orientifolds of Matrix theory and Noncommutative Geometry
• Noncommutative Geometry and Twisted Little-String Theories
• Morita Equivalence of Noncommutative Supertori
• Noncommutative fermions and Morita equivalence
• Mirror duality and noncommutative tori
• Twisted K-theory in $g>1$ from D-branes
• Compactified NCOS and duality
• Geometric foundations for classical $\mathrm{U}(1)$-gauge theory on noncommutative manifolds
• Twisted Conformal Field Theories and Morita equivalence
• Categories of holomorphic line bundles on higher dimensional noncommutative complex tori
• Global Seiberg-Witten maps for U(n)-bundles on tori and T-duality
• Morita equivalence of multidimensional noncommutative tori
• Quantization and Morita equivalence for constant Dirac structures on tori
• Strings, Dipoles and Fuzzy Spheres
• Fermionic T-duality and Morita Equivalence
• Strings, Noncommutative Geometry and the Size of the Target Space
• Classical gauge theory on quantum principal bundles
• Paired quantum Hall states on noncommutative two-tori
• Non-commutative Weitzenboeck geometry, gerbe modules, and WZW branes
• Noncommutative Riemann Conditions
• T-Duality Group for Open String Theory
• Morita equivalence of smooth noncommutative tori
• Strong Morita equivalence of higher-dimensional noncommutative tori
• A Remark On Field Theories On The Non-Commutative Torus
• On the Rosenberg-Zelinsky sequence in abelian monoidal categories
• Symmetry of Quantum Torus with Crossed Product Algebra
• Noncommutative tori, Yang-Mills and string theory
• Morita Equivalence and Interpolation of The Dirac-Born-infeld Theory on the Non-Commutative Torus
• From Surface Operators to Non-Abelian Volume Operators in Puff Field Theory
• Bloch waves and Non-commutative Tori of Magnetic Translations
• Dissipative quantum mechanics and Kondo-like impurities on noncommutative two-tori
• Noncommutativity Parameter As a Field on the String Worldsheet
• Classification of Connections on Higher-Dimensional Non-Commutative Tori
• Lectures on Symplectic Geometry, Poisson Geometry, Deformation Quantization and Quantum Field Theory