D-particles in the space-time of the shock wave

TL;DR

This paper investigates the interaction of two D-particles in a shock wave space-time, demonstrating consistency between string theory and matrix model approaches at different distance scales.

Contribution

It provides a detailed analysis of D-particle interactions in shock wave backgrounds, connecting string amplitude calculations with matrix model formulations.

Findings

At large distances, the amplitude matches supergravity predictions with (v^4) dependence.

The amplitude is independent of () at large distances, involving only massless modes.

The matrix model reproduces the string theory results in curved backgrounds.

Abstract

We study the interaction of two D-particles in the space-time of the shock wave. We first write the amplitude in string theory and find that, at large distances from the shock-wave source, the O(v^4) term in the relative velocity v is an \alpha'-independent function of the interbrane separation b. The amplitude is therefore that of supergravity--for large b, only closed-string massless modes contribute. We then show how the same result is obtained in the matrix model (at small b) by setting up the formulation of the dimensionally reduced super Yang-Mills theory in the curved background of the shock wave.