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

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 $D=3$ $\mathcal{N}=2$ 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 $\mathcal{M}(\mathcal{H})$ of the relative motion Hamiltonian $\mathcal{H}$, the counterpart of which enters the 4D nAmW action linearly. Curiously, the action possesses double supersymmetry also for an arbitrary function $\mathcal{M}(\mathcal{H})$. In particular for $\mathcal{M}=\text{const}$ we find a dynamical system describing the sum of single D$0$ action and the action of 1d dimensional reduction of the $D=3$ $\mathcal{N}=2$ SYM coupled to the worldline supergravity induced by the embedding of the center of energy motion into the $D=3$ $\mathcal{N}=2$ superspace.

JHEP style, 37 pages. V2: Misprints corrected. Cosmetic changes. V3. Misprints corrected, reference added, published version. V4: three misprints corrected

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Cited by in corpus (2)

• Complete nonlinear action for supersymmetric multiple D$0$-brane system
• Properties of multiple D0-brane system: 11D origin, equations of motion and their solutions