Transcribing Spacetime Data into Matrices

In certain supergravity backgrounds, D0 branes tend to polarize into higher dimensional Dp branes. We study this phenomenon in some generality from the perspective of a local inertial observer and explore polarization effects resulting from tidal-like forces. We find classically stable D2 brane droplets made of D0 branes and we are led to a local formulation of the UV-IR correspondence. A geometric Planck scale bound on the number of D0 branes plays an important role in the analysis. We focus on the impact of higher order moments of background fields and work out extensions of the non-commutative algebra beyond the Lie and Heisenberg structures. In this context, it appears that q-deformed algebras come into play. 1 [email protected]