3D supersymmetric nonlinear multiple D$0$-brane action and 4D counterpart of multiple M-wave system

TL;DR

This paper constructs a complete nonlinear action for multiple D0-branes in 3D superspace, derived via dimensional reduction from a 4D non-Abelian multiwave system, revealing double supersymmetry and connections to super Yang-Mills theory.

Contribution

It presents the first complete nonlinear multiple D0-brane action in 3D superspace, obtained from 4D multiwave models, and explores its supersymmetry properties and relation to super Yang-Mills theory.

Findings

Derived the nonlinear 3D multiple D0-brane action.

Showed the action's double supersymmetry for any function ${\

Linked the 3D action to 4D multiwave and 11D M-wave systems.

Abstract

Found is the complete nonlinear action of multiple D$0$-brane system (mD$0$) in three dimensional type II superspace which is invariant under rigid $D=3$ ${\cal N}=2$ spacetime supersymmetry and under local worldline supersymmetry generalizing the $\kappa-$symmetry of single D$0$-brane action. We show that a particular representative of this family of actions can be obtained by dimensional reduction of the action of $D=4$ non-Abelian multiwaves (nAmW), the $D=4$ counterpart of 11D multiple M-wave (mM0) action, that we have also constructed in this paper. This reduction results in an action with is nonlinear due to the presence of a certain function ${\cal M}({\cal H})$ of the relative motion Hamiltonian ${\cal H}$, the counterpart of which enters the 4D nAmW action linearly. Curiously, the action possesses double supersymmetry also for an arbitrary function ${\cal M}({\cal H})$. In particular for ${\cal M}=\text{const}$ we find a dynamical system describing the sum of single D$0$ action and the action of 1d dimensional reduction of the $D=3$ ${\cal N}=2$ SYM coupled to the worldline supergravity induced by the embedding of the center of energy motion into the $D=3$ ${\cal N}=2$ superspace.