The Gribov problem in noncommutative gauge theory

After reviewing Gribov ambiguity of non-Abelian gauge theories, a phenomenon related to the topology of the bundle of gauge connections, we show that there is a similar feature for noncommutative QED over Moyal space, despite the structure group being Abelian, and we exhibit an infinite number of solutions for the equation of Gribov copies. This is a genuine effect of noncommutative geometry which disappears when the noncommutative parameter vanishes.

Remarks on the eigenvalues distributions of D≤4 Yang–Mills matrix models

The phenomenon of emergent fuzzy geometry and noncommutative gauge theory from Yang–Mills matrix models is briefly reviewed. In particular, the eigenvalue distributions of Yang–Mills matrix models in lower dimensions in the commuting (matrix or Yang–Mills) phase of these models are discussed.

Field Equations and Radial Solutions in a Noncommutative Spherically Symmetric Geometry

We study a noncommutative theory of gravity in the framework of torsional spacetime. This theory is based on a Lagrangian obtained by applying the technique of dimensional reduction of noncommutative gauge theory and that the yielded diffeomorphism invariant field theory can be made equivalent to a teleparallel formulation of gravity. Field equations are derived in the framework of teleparallel gravity through Weitzenbock geometry. We solve these field equations by considering a mass that is distributed spherically symmetrically in a stationary static spacetime in order to obtain a noncommutative line element. This new line element interestingly reaffirms the coherent state theory for a noncommutative Schwarzschild black hole. For the first time, we derive the Newtonian gravitational force equation in the commutative relativity framework, and this result could provide the possibility to investigate examples in various topics in quantum and ordinary theories of gravity.