Relativistic Brane Scattering
Vijay Balasubramanian, Finn Larsen
TL;DR
The study addresses relativistic velocity dependence in large-impact-parameter scattering of D0-branes off p-branes, bridging supergravity, string theory, and Matrix theory via 11D uplift and open/closed string analyses. It develops a Hamilton-Jacobi semiclassical framework to compute phase shifts, demonstrates exact agreement with string theoretic results at large distances, and shows that naive nonabelian Born-Infeld or truncated Matrix theory fails to reproduce the full relativistic dependence. By analyzing bound states of 0- and 2-branes, it clarifies how Matrix theory captures leading kinematics but requires control of 1/n corrections to fully recover Lorentz-invariant supergravity results. The work highlights the subtle role of relativistic invariance and the limits of current nonperturbative formulations (M(atrix) theory) for relativistic brane dynamics. This provides a concrete, velocity-dependent benchmark for non-perturbative definitions of M-theory and directs future refinements in Lagrangians and 1/n corrections.
Abstract
We calculate relativistic phase-shifts resulting from the large impact parameter scattering of 0-branes off p-branes within supergravity. Their full functional dependence on velocity agrees with that obtained by identifying the p-branes with D-branes in string theory. These processes are also described by 0-brane quantum mechanics, but only in the non-relativistic limit. We show that an improved 0-brane quantum mechanics based on a Born-Infeld type Lagrangian also does not yield the relativistic results. Scattering of 0-branes off bound states of arbitrary numbers of 0-branes and 2-branes is analyzed in detail, and we find agreement between supergravity and string theory at large distances to all orders in velocity. Our careful treatment of this system, which embodies the 11 dimensional kinematics of 2-branes in M(atrix) theory, makes it evident that control of 1/n corrections will be necessary in order to understand our relativistic results within M(atrix) theory.