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

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.