Higher Order Spin-dependent Terms in D0-brane Scattering from the Matrix Model

TL;DR

This paper computes higher order spin-dependent terms in D0-brane scattering within the matrix model, extending previous results and demonstrating the method's applicability to more general Dp-brane interactions.

Contribution

It introduces a technique adapted to supersymmetry for calculating spin-dependent effects in D-brane scattering, specifically computing the $rac{v^2 \psi^4}{r^9}$ term.

Findings

The $rac{v^2 \psi^4}{r^9}$ term is successfully computed in the matrix model.

Results are compared with string theoretic calculations, showing consistency.

The method is adaptable to more general Dp-brane scattering scenarios.

Abstract

The potential describing long-range interactions between D0-branes contains spin-dependent terms. In the matrix model, these should be reproduced by the one-loop effective action computed in the presence of a nontrivial fermionic background $\psi.$ The $\frac{v^3 \psi^2}{r^8}$ term in the effective action has been computed by Kraus and shown to correspond to a spin-orbit interaction between D0-branes, and the $\frac{\psi^8}{r^{11}}$ term in the static potential has been obtained by Barrio et al. In this paper, the $\frac{v^2 \psi^4}{r^9}$ term is computing in the matrix model and compared with the corresponding results of Morales et al obtained using string theoretic methods. The technique employed is adapted to the underlying supersymmetry of the matrix model, and should be useful in the calculation of spin-dependent effects in more general Dp-brane scatterings.