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

TL;DR

Chepelev and Tseytlin address long-distance, low-velocity interactions involving a longitudinal $5$-brane bound state, testing three scattering configurations against the M(atrix) theory and supergravity descriptions. They develop a generalized classical probe method with nontrivial world-volume flux to model bound-state branes and compute leading velocity-dependent potentials in closed string theory, then reproduce these results in one-loop SYM for the same backgrounds, obtaining explicit phase shifts such as $\delta = \frac{n_0}{2 b^{2}}\big( N_4 v + \tfrac{1}{4} N_0 v^{3} \big)$ in the graviton--$4\Vert 0$ case. The results demonstrate precise agreement between the supergravity and M(atrix) theory pictures for all three configurations, including $0$-/$4\Vert 0$, $(2+0)$/$4\Vert 0$, and $(4\Vert 0)$–$(4\Vert 0)$ scatterings, thereby extending BFSS-type checks to 1/4 BPS bound states. The work provides a universal, flux-based probe framework to study bound-state interactions and reinforces the open/closed string duality and U-duality-driven descriptions of D-brane bound states in M(atrix) theory contexts.

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.