Relativistic Brane Scattering

TL;DR

This paper calculates relativistic phase-shifts for 0-branes scattering off p-branes using supergravity, confirming agreement with string theory at large distances and highlighting the limitations of current quantum mechanical models.

Contribution

It provides a detailed analysis of relativistic brane scattering, comparing supergravity results with string theory and quantum mechanics, and discusses implications for M(atrix) theory.

Findings

Supergravity phase-shifts match string theory predictions at large distances.

Non-relativistic quantum mechanics models fail to reproduce relativistic results.

Control of 1/n corrections is necessary for understanding relativistic effects in M(atrix) theory.

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.