3D supersymmetric nonlinear multiple D0-brane action and 4D counterpart of multiple M-wave system

Found is the complete nonlinear action of multiple D0-brane system (mD0) in three dimensional type II superspace which is invariant under rigid D = 3 𝒩 = 2 spacetime supersymmetry and under local worldline supersymmetry generalizing the κ -symmetry of single D0-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 ℳ(ℋ) of the relative motion Hamiltonian ℋ, the counterpart of which enters the 4D nAmW action linearly. Curiously, the action possesses double supersymmetry also for an arbitrary function ℳ(ℋ). In particular for ℳ = const we find a dynamical system describing the sum of single D0 action and the action of 1d dimensional reduction of the D = 3 𝒩 = 2 SYM coupled to the worldline supergravity induced by the embedding of the center of energy motion into the D = 3 𝒩 = 2 superspace.