Long-distance interactions of D-brane bound states and longitudinal 5-brane in M(atrix) theory

TL;DR

This paper analyzes long-distance interactions involving boosted M5-branes and D-branes, demonstrating agreement between supergravity and M(atrix) model calculations for various scattering configurations.

Contribution

It extends the classical probe method to bound states of D-branes, establishing the equivalence of supergravity and M(atrix) model results for interaction potentials.

Findings

Supergravity and M(atrix) model results agree for leading interaction terms.

Generalized probe method effectively treats bound states as probes.

Interaction potentials for various brane configurations are characterized.

Abstract

We discuss long-distance, low-velocity interaction potentials for processes involving longitudinally boosted M5-brane (corresponding in type IIA theory language to the 1/4 supersymmetric bound state of 4-brane and 0-brane). We consider the following scattering configurations: (a) D=11 graviton off longitudinal M5-brane, or, equivalently, 0-branes off marginal 4+0 bound state; (b) M2-brane off longitudinal M5-brane, or a non-marginal 2+0 bound state off marginal 4+0 bound state; (c) two parallel longitudinal M5-branes, or two 4+0 marginal bound states. We demonstrate the equivalence between the classical closed string theory (supergravity) and M(atrix) model (one-loop super Yang-Mills) results for the leading terms in the interaction potentials. The supergravity results are obtained using a generalisation of the classical probe method which allows one to treat bound states of D-branes as probes by introducing non-trivial world-volume gauge field backgrounds.