Moyal Deformations of Gravity via SU ( N ) Gauge Theories, Branes and Topological Chern-Simons Matrix Models

Moyal noncommutative star-product deformations of higher dimensional gravitational Einstein-Hilbert actions via lower-dimensional SU(\infty) gauge theories are constructed explicitly based on the holographic reduction principle. New reparametrization invariant p-brane actions and their Moyal star product deformations follows. It is conjectured that topological Chern-Simons brane actions associated with higher-dimensional "knots" have a one-to-one correspondence with topological Chern-Simons Matrix models in the large N limit. The corresponding large N limit of Topological BF Matrix models leads to Kalb-Ramond couplings of antisymmetric-tensor fields to p-branes. The former Chern-Simons branes display higher-spin W_\infty symmetries which are very relevant in the study of W_\infty Gravity, the Quantum Hall effect and its higher-dimensional generalizations. We conclude by arguing why this interplay between condensed matter models, higher-dimensional extensions of the Quantum Hall effect, Chern-Simons Matrix models and Gravity needs to be investigated further within the framework of W_\infty Gauge theories.