The charge radius of a Dpbrane

TL;DR

This paper explores a fundamental limit on the localization of Dp-brane charge, linking tachyon condensation, string theory stability, and a minimal radial distance related to the brane's charge and string parameters.

Contribution

It introduces a minimal charge radius for Dp-branes derived from stability considerations, connecting tachyon condensation to a charge uncertainty relation.

Findings

Identifies a minimal radial coordinate r_c for Dp-branes.

Shows that at r_c, curvature and field gradients are of order 1/α'.

Proposes a stability bound as an uncertainty relation for D-brane charge.

Abstract

Sen has shown that tachyon condensation in Dbrane-anti-Dbrane configurations can lead to remarkable connections between string theories. A consequence of his results is that there is a minimal value of the radial coordinate $r_{c} \propto \sqrt{\alpha'} (gN)^{1/(9-p)}$ such that N units of D$p$brane charge cannot be localized to values smaller than $r_{c}.$ At this value of $r_{c}$ the curvature and the gradient of the Ramond-Ramond field strength are of order $1/\alpha',$ and the vacuum, regarded as a Dbrane-anti-Dbrane configuration with a tachyon condensate, is rendered unstable, leading to a separation of the Dbrane and the anti-Dbrane. This value of $r_{c}$ lies in the region intermediate between the near-horizon regime and the asymptotic regime for Dbrane classical solutions for small $g$. This vacuum stability bound on the curvature can be interpreted as an uncertainty relation for Dbrane charge.