The Lorentz force between D0 and D6 branes in string and M(atrix) theory

TL;DR

This paper investigates the Lorentz force between D0 and D6 branes in string and M(atrix) theory, revealing a velocity-linear term from R-R odd spin structure that was previously overlooked.

Contribution

It introduces a new analysis showing the Lorentz force term in the D0-D6 system using boundary states and M(atrix) theory, correcting prior omissions.

Findings

Identifies a velocity-linear Lorentz force term in the D0-D6 system.

Demonstrates the term arises from R-R odd spin structure.

Validates the result through both string and M(atrix) theory calculations.

Abstract

We use different techniques to analyze the system formed by a D0 brane and a D6 brane (with background gauge fields) in relative motion. In particular, using the closed string formalism of boosted boundary states, we show the presence of a term linear in the velocity, corresponding to the Lorentz force experienced by the D0 brane moving in the magnetic background produced by the D6 brane. This term, that was missed in previous analyses of this system, comes entirely from the R-R odd spin structure and is also reproduced by a M(atrix) theory calculation.