Four-Brane and Six-Brane Interactions in M(atrix) Theory

TL;DR

This paper investigates how four-brane and six-brane configurations can be realized in M(atrix) theory and tests their interactions with gravitons and membranes by computing velocity-dependent potentials. Using a one-loop matrix-model calculation around bound-state backgrounds with zero-branes, it derives phase shifts for zero-brane scattering and compares them to corresponding short-distance type IIa string theory results, finding exact agreement in the configurations studied. The long-distance behavior is recovered because these setups are near-supersymmetric, yielding consistent $b^{-3}$ or $b^{-1}$ potentials as appropriate. The work also clarifies that a pure six-brane bound-state with zero-branes is obstructed and requires additional branes to bind, while four-branes can form threshold bound states, supporting the proposed matrix-theory description of these branes and their Type IIA correspondence.

Abstract

We discuss the proposed description of configurations with four-branes and six-branes in m(atrix) theory. Computing the velocity dependent potential between these configurations and gravitons and membranes, we show that they agree with the short distance string results computed in type IIa string theory. Due to the ``closeness'' of these configuration to a supersymmetric configuration the m(atrix) theory reproduces the correct long distance behavior.