Teleparallel Gravity and Dimensional Reductions of Noncommutative Gauge Theory

TL;DR

This paper demonstrates how dimensional reductions of noncommutative electrodynamics naturally produce a teleparallel gravity framework, linking noncommutative gauge theories to general relativity with potential string theory corrections.

Contribution

It shows that noncommutative gauge fields can induce a teleparallel geometry equivalent to general relativity, with a specific relation between the Planck length, coupling constant, and noncommutativity scale.

Findings

Noncommutative gauge fields lead to Weitzenbock geometry.

The induced gravity theory is equivalent to teleparallel gravity.

Higher-curvature and non-local terms resemble string theory effects.

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.