Complete nonlinear action for supersymmetric multiple D$0$-brane system

TL;DR

This paper develops a comprehensive nonlinear action for multiple D0-branes that incorporates supersymmetry and worldline symmetry, extending the single-brane model and connecting to eleven-dimensional M-wave systems.

Contribution

It introduces a complete nonlinear action for multiple D0-branes with both target space and worldline supersymmetry, including an arbitrary function of the relative motion Hamiltonian.

Findings

The action generalizes single D0-brane dynamics to multiple branes.

It maintains supersymmetry and kappa-symmetry in the multi-brane context.

Special cases relate to dimensional reduction from M-theory.

Abstract

We present a complete nonlinear action for the dynamical system of nearly coincident multiple D$0$-branes (mD$0$) which possesses, besides manifest spacetime (target superspace) supersymmetry, also the worldline supersymmetry, a counterpart of the local fermionic $\kappa$-symmetry of single D$0$-brane (Dirichlet superparticle). The action contains an arbitrary non-vanishing function ${\cal M}({\cal H})$ of the relative motion Hamiltonian ${\cal H}$. The $D=10$ mD$0$ model with particular form of ${\cal M}({\cal H})$ can be obtained by dimensional reduction from the action of eleven-dimensional ($D=11$) multiple M-wave (mM$0$) system.