Non-abelian action of D0-branes from Matrix theory in the longitudinal 5-brane background

TL;DR

This paper derives the non-abelian effective action of D0-branes in a longitudinal 5-brane background using Matrix theory, testing the coupling to weak backgrounds and ensuring consistency between different Matrix theory formulations.

Contribution

It provides a novel derivation of D0-brane couplings to 5-brane backgrounds within Matrix theory, including analysis of matrix ordering subtleties.

Findings

Coupling to 5-branes aligns with previous proposals

Identifies subtleties in matrix ordering for multipole moments

Validates consistency between Matrix theory formulations

Abstract

We study one-loop effective action of Berkooz-Douglas Matrix theory and obtain non-abelian action of D0-branes in the background field produced by longitudinal 5-branes. Since these 5-branes do not have D0-brane charge and are not present in BFSS Matrix theory, our analysis can be regarded as an independent test for the coupling of D-branes to general weak backgrounds proposed by Taylor and Van Raamsdonk, and also as a check of consistency between the two versions of Matrix theory. The coupling to the 5-branes which we obtain is basically consistent with the previous proposal, but we point out subtleties in the ordering of matrices for the multipole moments.