Transcribing spacetime data into matrices

TL;DR

This paper investigates how D0 branes polarize into D2 branes in supergravity backgrounds, revealing new algebraic structures and a local UV-IR correspondence influenced by higher order background moments.

Contribution

It introduces a local formulation of the UV-IR correspondence and explores the role of q-deformed algebras in D-brane polarization phenomena.

Findings

D2 brane droplets can form at extremum of Born-Infeld action without RR fields

A holographic Planck scale bound constrains the number of D0 branes

Higher order moments lead to extensions of non-commutative algebra, including q-deformations

Abstract

In certain supergravity backgrounds, D0 branes may 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 D2 brane droplets made of D0 branes at an extremum of the Born-Infeld action even in scenarios where the RR fields may be zero. These solutions lead us to a local formulation of the UV-IR correspondence. A holographic 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.