Properties of multiple D0-brane system: 11D origin, equations of motion and their solutions

TL;DR

This paper explores the properties of multiple D0-brane systems, deriving their equations of motion from 11D M-wave systems, and establishes a correspondence between their solutions and supersymmetric Yang-Mills theory.

Contribution

It introduces a complete supersymmetric action for mD0 systems with arbitrary nonlinear functions and links their equations of motion to 11D M-wave systems and SYM solutions.

Findings

Derived equations of motion for mD0 with arbitrary ${ m M}({ m H})$

Established correspondence between mD0 solutions and SYM solutions

Showed supersymmetric solutions coincide between systems

Abstract

We study the properties of 10D multiple D0-brane (mD0) system described by recently proposed complete supersymmetric and $\kappa$-symmetric nonlinear action which includes an arbitrary positive definite function ${\cal M}({\cal H})$ of the relative motion Hamiltonian ${\cal H}$. First we show how the action with a particular nonlinear ${\cal M}({\cal H})$ can be obtained from the action for 11D multiple M-wave (multiple M0-brane or mM0) system. Then we obtain the complete set of equations of motion of mD0 system with arbitrary positive definite ${\cal M}({\cal H})$, perform a convenient gauge fixing, solve the center of energy equations and establish an interesting correspondence between the relative motion mD0 equations and the equations of maximal supersymmetric SU(N) Yang-Mills theory (SYM). We show that this correspondence does not imply a gauge equivalence but establishes a relation between solutions of the system. In particular, it implies that all the supersymmetric solutions of mD0 equations in its relative motion part coincide with supersymmetric solutions of the SYM equations.