Transcribing spacetime data into matrices

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 BornInfeld 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.

Scrambling with matrix black holes

“…0, the spherical configuration is unstable, albeit with a long lifetime for large N [27]. One can stabilize it by adding a mass term to the Lagrangian of the form m 2 TrX 2 ; physically, this is achieved by putting the D0-branes in a nontrivial supergravity background where m 2 is mapped onto local tidal forces experienced by the D0-branes [28]. 2 For simplicity, we imagine the background compactified to 3 þ 1 dimensions; we do this by freezing the dynamics in the Y a directions, setting y a ¼ 0 by hand.…”

Branes wrapping black holes as a purely gravitational dielectric effect

“…This means that our configurations are in a sense time dependent (although at the level of the effective action for the gravitational waves we do not see it, since the momentum is added as N T 0 by construction). We believe that the configurations presented in this paper are nice examples of the ones proposed in [10]. In any case, we should point that, contrary to the configurations analyzed in [10], ours are wrapping non-contractible cycles.…”

Generally Covariant Actions for Multiple D-branes

“…Finally, it will be interesting to understand whether the class of generally covariant actions presented here (or a more restricted class that takes into account additional constraints) predicts any interesting generic phenomena for D-branes on curved spaces, such as a gravitational version of the dielectric effect [24,25,26,27].…”

“…Thus, all of the arbitrary coefficients in V appear in the transformation law, as we should expect, since we have already fixed any ambiguity associated with transformation of the type (24) by assuming all pure tensor terms in ∆(V ) vanish. Various possible interpretations for these arbitrary coefficients are suggested in section 3.…”