Teleparallel Gravity and Dimensional Reductions of Noncommutative Gauge Theory

Abstract

We study dimensional reductions of noncommutative electrodynamics on flat space which lead to gauge theories of gravitation. For a general class of such reductions, we show that the noncommutative gauge fields naturally yield a Weitzenbock geometry on spacetime and that the induced diffeomorphism invariant field theory can be made equivalent to a teleparallel formulation of gravity which macroscopically describes general relativity. The Planck length is determined in this setting by the Yang-Mills coupling constant and the noncommutativity scale. The effective field theory can also contain higher-curvature and non-local terms which are characteristic of string theory. Some applications to D-brane dynamics and generalizations to include the coupling of ordinary Yang-Mills theory to gravity are also described.

31 pages LaTeX; References added

References in corpus (7)

• How Noncommutative Gauge Theories Couple to Gravity
• Geometry of the Gauge Algebra in Noncommutative Yang-Mills Theory
• Supermatrix Models
• Supergravity couplings to Noncommutative Branes, Open Wilson Lines and Generalised Star Products
• Gauge theories of spacetime symmetries
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• Gravity and the Structure of Noncommutative Algebras
• Emergent Spacetime and The Origin of Gravity
• Gravity as a Quantum Effect on Quantum Space-Time
• Gauge theories on quantum spaces
• Teleparallel Complex Gravity as Foundation for Noncommutative Gravity
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• Higher-spin gravity and torsion on quantized space-time in matrix models
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• Poisson electrodynamics on $\kappa$-Minkowski space-time
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