Super Yang-Mills on the Noncomutative Torus

Abstract

After a brief review of matrix theory compactification leading to noncommutative supersymmetric Yang-Mills gauge theory, we present solutions for the fundamental and adjoint sections on a two-dimensional twisted quantum torus in two different gauges. We also give explicit transformations connecting different representations which have appeared in the literature. Finally we discuss the more mathematical concept of Morita equivalence of C*-algebras as it applies to our specific case.

22 pages, LaTeX, to appear in the Arnowitt Festschrift Volume ``Relativity, Particle Physics, and Cosmology'', Texas A&M University, April 1998, published by World Scientific; references added

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• A Large-N Reduced Model as Superstring
• Morita equivalence and duality
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Cited by in corpus (25)

• Introduction to M(atrix) theory and noncommutative geometry, Part II
• Introduction to M(atrix) theory and noncommutative geometry
• Nonabelian noncommutative gauge theory via noncommutative extra dimensions
• Dipoles, Twists and Noncommutative Gauge Theory
• Quantum Mechanics on the Noncommutative Torus
• Dualities of the Matrix Model from T-Duality of the Type II String
• Noncommutative geometry and physics: a review of selected recent results
• Gauge Bundles and Born-Infeld on the Noncommutative Torus
• BPS states on noncommutative tori and duality
• Casimir Effect on the Radius Stabilization of the Noncommutative Torus
• Noncommutative String Theory, the R-Matrix, and Hopf Algebras
• A Note on the BPS Spectrum of the Matrix Model
• Compactification of M(atrix) theory on noncommutative toroidal orbifolds
• World Volume Noncommutativity versus Target Space Noncommutativity
• Constructions of Non Commutative Instantons on $T^4$ and $K_3$
• Lowest Landau level theory of the bosonic Jain states
• Derivatives and the Role of the Drinfel'd Twist in Noncommutative String Theory
• Homological mirror symmetry on noncommutative two-tori
• D0-branes in an H-field Background and Noncommutative Geometry
• Noncommutative Deformation of Instantons
• Star product formula of theta functions
• Matrix Compactification On Orientifolds
• T-Duality Group for Open String Theory
• Approximation of Quantum Tori by Finite Quantum Tori for the Quantum Gromov-Hausdorff Distance
• Non commutative geometry for outsiders; an elementary introduction to motivations and tools